The Eleatic philosophers left a very troublesome problem for the Presocratics that followed them: how is it possible to think of the sensible world when it has been demonstrated beyond reasonable doubt that it is not possible to do so? In contrast with the Milesians, who sought to define the world as we experience it, the Eleatic Parmenides downplayed the sensual world's importance and ultimately negated it entirely, calling for a retreat into the realm of pure reason to wholly understand the question of what it is to be. Empedocles took up the aspects of Eleatic philosophy that require stability of being, but he himself was not strictly a follower of Parmenides (as, say, Zeno was) because he attempted to re-evaluate and eventually preserve the sensible world, instead of merely casting it aside as being so much foolish opinion as Parmenides did.
Parmenides held it that being itself was by necessity a unity, and an eternal one at that; "the one, that it is and that it is not possible for it not to be" is the only truth that is really possible to learn, since "neither may [one] know that which is not [...]/nor may [one] declare it" (Presocratics Reader, 45-6, no. 2). In other words, being is, always was, and always will be; not-being is not, never was, and never will be; and beyond that it is not possible to say anything more on the matter without straying into nonsense.
How could what is be in the future? How could it come to be?
For if it came into being, it is not, nor if it is ever going to be.
In this way, coming to be has been extinguished and destruction is unheard of.
Nor is it divided, since it all is alike
nor is it any more in any way, which would keep it from holding together,
or any less, but it is all full of what is.
Therefore, it is all continuous, for what is draws near to what is. (47-8, no. 8)
We can think of the Parmenidean doctrine as being the result of a desire to express the overarching continuity of nature as a whole, instead of the dizzying multiplicity that we are met with upon attempting to contemplate it as a collection of individuals (like conceiving of the archetype of a given thing, rather than an instance of it). This way it becomes easier to see why Parmenides might have thought that such an argument was necessary and valuable: there had to be some way to reconcile the way that nature seems to continue on -- with like springing from like, with the propagation and permanence of so many species -- despite the fact that all things seem to die, to be replaced by other things. So the world as we can experience it is somehow both continuous and discontinuous, simultaneously. And since these two are polar opposites, it is very difficult to conceive of them both being true; thus one of them must be false. Parmenides says that is the experience of nature as discontinuous, as ever-changing and multiple, which is untrue: he calls it "doxa" -- opinion, or belief -- and proposes instead that the reality of things can only be found in thinking nature instead of experiencing it sensually. It is in thinking instead of feeling that we can come to an understanding of the one, static and immutable: for "[s]uch, unchanging, is that for which as a whole the name is 'to be' " (51, no. 19).
This is the beginning point for Empedocles, and the problem that he attempted to resolve: how the logical necessity for unity (in Parmenidean terms) can be reconciled with the undeniable fact that when we look at the world, we see it changing before our very eyes. In many ways, his solution incorporates the suppositions that underlie the question it addresses, recycling the unchanging unity of being into something that Parmenides himself would not necessarily agree with but would nonetheless have trouble refuting.
The point where Empedocles strays a great distance from Parmenides, and indeed the starting point for his eventual recovery of the sensible world, is that he allows for the existence of four elements instead of just one unified being. These elements -- "fire and water and earth and the immense height of air" -- are unchanging in and of themselves, but under the influences of the motive forces Love and Strife they can combine, break apart, and recombine in various configurations to form different substances (62, no. 32). But the four elements are not precisely un-Parmenidean. They all partake in what Parmenides held to be the essential qualities of being -- they are eternal, having never come to be and never to pass away, and immutable, since they themselves are not subject to change:
For these [the four elements] are all equal and of the same age,
but each rules in its own province and possesses its own individual character,
but they dominate in turn as time revolves.
And nothing is added to them, nor do they leave off,
For if they were perishing continuously, they would no longer be.
But what could increase this totality? And where would it come from?
And how [or, where] could it perish, since nothing is empty of these?
But there are just these very things, and running through one another
at different times they come to be different things and yet are always and continuously the same. (64, no. 32)
Moreover, Empedocles holds it that the elements themselves are not condemned to be discrete things forever; indeed, "at one time they grow to be only one/out of many, but at another they grow apart to be many out of one" (63, no. 32) -- such that together they are occasionally fully in agreement with Parmenides' requirement for the unity of being, even if we do not accept the proposition that the four elements by themselves are parts of one being.
Empedocles is also preoccupied with opposites: this is perhaps a relic of Parmenides' insistence that all opposition is logically contradictory within the larger framework of being-as-one. Apart from the above, where the one grows into many as the many become one, the opposition that comes under especially close scrutiny is that of birth and death (or, creation and destruction) which simply does not exist in Parmenidean terms (since not-being cannot be). Empedocles treats them slightly differently than Parmenides would have: he says that "the coming together of all things produces one birth and destruction,/and the other is nurtured and flies apart when they grow apart again./And these never cease continually interchanging" (63, no. 32). It is true that this shows an opposition, but it is one in which each side is always already becoming the other. It thus negates itself and becomes a unity again, even in its opposition:
They [i.e., the four elements] dominate in turn as the cycle revolves,
and they decrease into one another and grow in their turn, as destined.
For there are just these things, and running through one another
... they grow together into one, the whole, and become subordinate (68, no. 50).
Thus Empedocles allows for what seems to our senses to be creation and destruction, comings-to-be and passings-away in the world, because even as something is destroyed the elements that comprised it are being appropriated by Love to create something new. He might have argued that this is not creation or destruction as Parmenides defined them -- negations of being, and nonsense -- precisely because of the re-creative process: the material stuff that makes up whatever it was that has been destroyed has not itself been destroyed, nor has the new created thing sprung up out of nowhere. Both are merely a rearranging of already-extant material, in the form of the four elements. But the elements are not in isolation from each other; instead, taken together they comprise the totality of being itself that stood at the core of Parmenides' doctrine.
In this way, by giving us the ability to think the world in the rational terms of the Eleatics without contradicting and compromising our sensual impressions of it, Empedocles can be thought to have succeeded in restoring the sensible world to its rightful place alongside the intelligible.
It is rarely entirely fair to speak of the Presocratics as somehow demonstrating a clear progression in thought from each philosopher to the next. Any categories we might attempt to slot them into are probably false, and would probably be alien to them. Nonetheless, doing so anyway can prove very useful for our understanding of what each philosopher was trying to get at; it's helpful to compare opposing points of view, because by picking out the differences we can begin to see each argument more clearly.
Page references above come from A Presocratics Reader, ed. Patricia Curd. Indianapolis: Hackett Publishing Company, 1995.