In the age before Parmenides, Empedocles would not have had to posit the two motive forces. To explain why his elements mixed and separated, he would merely have referred flippantly to eternal motion. In the face of Parmenides' challenge to the very existence of change, however, philosophers could no longer take change and motion for granted. Empedocles, like those who came after him, was forced to both explain what he meant by change and to give a very specific account (by Presocratic standards) of how change occurs.
He, therefore, posited the two motive forces of love and strife. These forces are corporeal, or physical. Their main role is to cause the elements to mix in their proper ratios. Love causes them to mix, strife to separate.
Empedocles speaks about the motive forces as if they really were emotions. He often says that the elements yearn for each other and then come together, or that they get angered and separate. But this is almost certainly just a metaphorical way of speaking; it is very doubtful that he personified his natural world to such a degree. How exactly the motive forces were meant to work, though, if not as motivating emotions, is entirely unclear. Perhaps Empedocles did not think out his theory that far, or perhaps we simply do not have the relevant passages.
As far as the equilibrium of the cosmos is concerned, Empedocles seems torn between the placid state of Anaximander and the fiery state of Heraclitus. The cosmos, as Empedocles envisions them, go through long cycles during which one or the other of the motive forces dominates. When the force of love is in control the universe tends toward harmony, and diversity begins fading; sometimes the universe reaches such a harmonious state that the only diversity remaining is that of the original four elements. When, on the other hand, the individuating force of strife is in control, there is tension between opposites; in this state, objects, qualities, and properties begin to increasingly individuate themselves.
In describing the state and operations of the cosmos, Empedocles floats a theory of the origin of species that hits startling close to Darwinian natural selection. Many species, he explains, arose early on by sheer chance, through the mixing of the elements by love. Only some of these, though, were adapted to survival. Those that were best adapted survived and passed on their characteristics to later generations. Those that were not well-adapted, simply died before propagating. His examples of maladaptive species are particularly fun to thumb through, since they read like descriptions of characters from a goofy, over-stuffed science fiction parody: neckless faces, arms without shoulders, eyes in need of foreheads, men with faces on both sides, ox-men, and androgynous beings.