In thermodynamics, motive power, or "puissance motive", in French, refers to the work associated with lifting a weight through a height, done cyclically; hence "work per unit time" or "force moving an object per unit distance per unit time"; or moving power.

Overview
In 1690, Denis Papin, in hisA New Method to Obtain Very Great Motive Powers at Small Cost”, in reference to his new theoretical heat engine (see: Papin engine), was employing the term "motive power" in reference to the ability of fire to raise weight, cyclically. [1]

In 1824, Sadi Carnot, in his On the Motive Power of Fire, employed the term as follows: [2]

“We use here the expression ‘motive power to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, a measure, the product of the weight multiplied by the height to which it is raised.”

In equation format, if this "motive power" were taken as the measure of this "useful effect" done in one cycle, Carnot would have been referring to work, in modern terms:

$W = mgh\,$

If, however, he were referring to the amount of this "useful effect" done by a heat engine for a number of cycles, say in one hour, then he would be referring to motive power as "power" or rate of work done per unit time:

$P = \frac{mgh}{t}\,$

which would have been equivalent to the number of pounds of water the steam engine could pump or lift out of a flooded mine in a specific amount of time.

Quotes
The following are related quotes:

Heat is nothing but motive power, or rather motion, which has changed form. It is motion of the particles of bodies. Whenever motive power is destroyed, there is a simultaneous production of an amount of heat exactly proportional to the motive power that is destroyed. Conversely, whenever there is destruction of heat, motive power is produced. Hence, we may state, as a general proposition, that the quantity of motive power in nature is fixed, and that, strictly speaking, motive power is neither produced nor destroyed. It is true that it changes its form, that is, it sometimes produces one kind of motion, sometimes another. But it is never annihilated.”
Sadi Carnot (c.1827), manuscript III (F° 7 recto); posthumously deposited to the French Academy of Sciences by M.H. Carnot in 1878; Robert Fox (1986) translation [3]

References
1. (a) Papin, Denis. (1690). “A New Way to Obtain Very Great Motive Powers at Small Cost” (Nova Methodus ad Vires Motrices Validissimas levi Pretio Comparandas). Acta Eruditorum, anno, Aug., pgs. 410-14.
(b) Muirhead, James. (1859). The Life of James Watt, (English translation: Ch. XI, Denys Pain: His memoir of 1690, Section: A New Way to Obtain Very Great Motive Powers at Small Cost”, pgs. 131-42). London: John Murray.
(c) The original Latin, accompanied by a translation, in Muirhead’s Mechanical Inventions of James Watt, Vol. III., pg. 139.
2. Carnot, Sadi. (1824). “Reflections on the Motive Power of Fire and on Machines Fitted to Develop that Power.” Paris: Chez Bachelier, Libraire, Quai Des Augustins, No. 55.
3. (a) Carnot, Sadi. (c.1827). "Notes on Mathematics, Physics, and Other Subjects", Archives of the Academy of Sciences, Paris.
(b)
Fox, Robert. (1986). Reflections on the Motive Power of Fire: a Critical Edition with the Surviving Scientific Manuscripts (heat quote, pgs. 26, 191). Manchester University Press.