In science, drive, from the PIE dhreibh- “pushing from behind”, push meaning "to press against with force", is a cause to move by force or compulsion. 
In a psychological sense, drive is the motive force or motivational factor behind a person’s actions; or a basic compelling urge.  The opening quote to American psychologist Paul Young’s 1936 book Motivation of Behavior, chapter “The Energetics of Activity”, is by American gifted-children psychologist Florence Goodenough, which summarizes the his views on the word drive: 
“The literal meaning of motivation (drive) is the process of induced movement.”
In terms of the modern understanding of this definition of drive, one must compare the mechanism or photon-induced movement of the 3-element retinal molecule to the photon-induced movement of the 26-element human molecule, a process colloquially known as “free will”. 
The word “drive”, which has been widely used in discussions of motivation, came into use in psychology via the publication of American psychologist Robert Woodworth’s 1918 publication Dynamic Psychology, and from this source it was taken up by the animal psychologists.  According to Woodworth:
“Once the point of view of a dynamic psychology is gained, two general problems come into sight, which may be named the problem of ‘mechanism’ and the problem of ‘drive’.”
He continues, “one is the problem, how we do a thing, and the other is the problem of what induces us to do it. Take the case of the pitcher in a baseball game. The problem of mechanism is the problem of how he aims, gauges distance and amount of curve, and coordinates his movements to produce the desired end. The problem of drive induces such questions as to why he is engaged in the exercise at all, why he pitches better one day than on another, why he rouses himself more against one than against another batter, and many similar questions.” Woodworth, according to American psychologist Paul Young, derived the term “drive” from mechanics; in that: 
“A machine must be driven if it is to move, and the drive of a machine is the supply of energy that puts the mechanism in motion.”
In extrapolation, the same definition applies in the human case. The “supply of energy that puts the mechanism in motion” in the human scenario, however, is very complicated, depending on detailed description of valence shell photon-electron interactions in the periphery sensory system of a set of persons in a system owing to the influx of photons from the sun.  In terms of etymology of the term “drive”, in the mind of Woodworth, in a personal communication from Woodworth to Young, he states:
“I believe you are right in supposing that the current use of ‘drive’ in animal psychology and other psychology springs from my use of the word in Dynamic Psychology, 1918. I am sure I did not derive the word from any previous psychologist. I got it from mechanics. A machine has a mechanism, such that if it is put in motion it operates in a certain way; but it must be driven in order to move. The ‘drive’ of a machine is the supply of energy that puts it in motion.”
Moss’ eight-principles of drives and resistances
The animal psychologists took up the word, according to Young, because “it carried no implications of conscious motive.” The first to use the term in animal psychology was American physician Fred Moss who published his 1924 PhD dissertation “A Study of Animal Drives”, in which he introduced his “resistance” apparatus for measuring the drive in terms of the amount of resistance (electric shock) which it would overcome.  This usage was taken up by others in the decade to follow. Moss wrote to Young that he was familiar with “dynamic psychology”, though he did not definitely recall adopting the word from Young. He used the term drive, according to Young: 
“[drive (term use)] not to describe any instinct or necessary inborn condition in the animal, but to describe a certain set of chemical conditions that make the animal move in a definite direction in the same way that the explosion of gas in the chamber of the automobile makes the piston move up and down.”
The basic thesis of Moss’ 1924 paper is that: “the behavior of any animal is the result of his drives to action and the opposing resistances”.  Drives, according to Moss, are “impelling forces” in the situation that stimulate the animal to positive behavior, e.g., the hunger drive impels to food-seeking; the maternal drive impels the mother to go to the young, especially when they show distress. Resistances, according to Moss, are “repelling forces” that stimulate to negative behavior; e.g., the presence of cats repels rats; and again, if rats are placed in a maze the floor of which is covered with crushed ice, they avoid the cold and seek the relative warm, dry goal-box. On these outlines, and other experiments, Moss drew up a series of eight-principles of a dynamic theory of drives and resistances, which are in short:
P1. Any animal drive may be measure in terms of resistances.
P2. A successful drive is, by definition, stronger than the resistance overcome.
P3. If two independent drives are opposed by the same resistance and one drive overcomes the resistance while the other fails, the one that overcomes the resistance is the stronger drive.
P4. Given two drives both functioning at the same time, and so arranged that neither can succeed without neglecting the other, the one that succeeds is the stronger drive.
P5. Given two antagonistic resistances both functioning at the same time and both so arranged that neither can cease to function without overcoming the other, the one that over comes is the stronger resistance.
P6. When one drive by itself is not strong enough to overcome a resistance, it may be reinforced by other drives, until it is strong enough to overcome the resistance.
P7. As a motive force is provoking the learning of such problems as a maze, the drive is strongest which causes the animal to learn the problem in the shortest time and with the fewest errors.
P8. Other things being equal, every time a resistance is overcome, the strength of the resistance is weakened.
Following Woodworth and Moss, the term “drive” was employed by Dashiell, Tolman, Richter, Warden, Stone, and others, until, by 1936, the word had become common in animal psychology other elementary textbooks. In 1943, American behavioral physiologist Clifford Morgan defined drive or motivation as “a central neural state of an organism”.  Also that year, noted American psychologist Clark Hull, life’s work was to explain learning and motivation by scientific laws of behavior, arrived at the conclusion that: “fundamentally, drives energize behavior” 
In his development of psychodynamics, Austrian psychoanalyst Sigmund Freud, in his writings about the "engines of human behavior", used the German word Trieb, a word that can be translated into English as either instinct or drive.  The German, prior to the 1930s, had used the word “Trieb” both for the drive of a machine and for animal impulse. 
In chemistry and human chemistry, the driving force or affinity A of a reaction or human chemical reaction is the decrease in Gibbs free energy on going from the reactants to the products of a chemical reaction (-ΔG). 
In terms of a biochemical or neurochemical appoach to understanding "drive", in recent years, scientists have begun looking at a number of key internal motivators, in particular dopamine, often called the "drive" chemical. 
1. (a) Drive – Dictionary.com (based on the Random House Unabridged Dictionary, 2006).
(b) Drive – EtymOnline.com.
2. Drive (definition) – Stedman’s Medical Dictionary (1995), 26th Edition.
3. Young, Paul T. (1936). Motivation of Behavior – the Fundamental Determinants of Human and Animal Activity, (ch. 2: “The Energetics of Activity”, pg. 70-73. New York: Wiley.
4. Thims, Libb. (2007). Human Chemistry (Volume One), (pg. 198: “Retinal molecule reacts to a photon”), (preview). Morrisville, NC: LuLu.
5. (a) Young, Paul T. (1936). Motivation of Behavior – the Fundamental Determinants of Human and Animal Activity, (ch. 2: “The Energetics of Activity”, pg. 70-73). New York: Wiley.
(b) Woodworth, Robert Sessions. (1918). Dynamic Psychology, (ch. VII: “Drive and Mechanism in Abnormal Behavior”, pg. 167; ch. VIII: “Drive and Mechanism in Social Behavior”, pg. 192). New York: Columbia University Press.
6. Moss, Fred A. (1924). “Study of Animal Drives”, J. Exp. Psychol. 7, 165–185.
7. Morgan, Clifford T. (1943). Physiological Psychology. New York: McGraw-Hill.
8. Hull, Clark L. (1943). Principles of Behavior. New York: Appleton-Centry-Crofts.
9. Walsh, Anthony (1991). The Science of Love - Understanding Love and its Effects on Mind and Body. Buffalo, New York: Prometheus Books.
10. (a) Driving force (affinity) of a reaction – IUPAC Gold Book.
(b) Thims, Libb. (2007). Human Chemistry (Volume One), (see: "driving force", index), (preview), (Google books). Morrisville, NC: LuLu.
(c) Thims, Libb. (2007). Human Chemistry (Volume Two), (see: "driving force", index), (preview), (Google books). Morrisville, NC: LuLu.
11. Pfaff, Donald W. (1999). Drive - Neurobiological and Molecular Mechanisms of Sexual Motivation. Cambridge, Mass.: The MIT Press.
● Vermorel, Madeleine. (1990). “The drive (Trieb), from Goethe to Freud.” International Review of Psychoanalysis, 17, 249-56.