Humans unknowingly create immortal, sentient beings (toys) for the sole purpose of entertaining their children. These toys then keep up the charade of their non-existence for your benefit. Mostly.
Unlike in many toys-coming-to-life tales, there is no magic. To the audience's knowledge, the toys are not brought to life by curses, voodoo, spells, or a racist cupboard. It is implied that they are alive straight from the factory (or at least from the toy store).
According to the end of the first movie, it is possible for them to communicate with humans, it's just "against the rules".
The rules appear to be a set of instinctual values all toys abide by. Even toys that think they are just really tiny humans (or something?) as seen in Buzz Lightyear, follow them automatically. As soon as humans are present, they return to the location the human last left them (if possible) and become motionless, to give the appearance of being inanimate.
Toy Story takes a brave stance on many controversial issues, such as Andy's mom being a single parent, or whether or not straight men should wear ascots. But the most controversial topic tackled by the series is, by far, the issue of slavery.
The toys seem to thrive when being frequently used as human children's playthings, fulfilling a purpose that they cannot get from other relationships. Interacting only with other toys seems to lead to depression, and sometimes even homicidal tendencies, as was the case with the Prospector.
However, the relationship between humans and toys is far from symbiotic.
There is no contention among any characters that toys are the property of their owner-children. In fact, their relationship parallels many slave and master situations throughout history:
Toys are bought and sold as a commodity; despite clearly being sentient, rational, and intelligent to the audience, possibly even more intelligent than their masters, they are considered below all humans and subject to their whims. They have no choice in their living arrangements, relationships (toys do not reproduce sexually, but do pair off romantically) are often interrupted or severed entirely when one member of the pair is sold or given away to a new owner, "sick" or "injured" toys are sold or disposed of, and most shockingly, can be tortured, mutilated, or murdered by their owner without any recourse.
Some deserve it more than others.
The only time in which toys use human agency (for lack of a better phrase) in order to demand rights is in the first movie, where they "break the rules" and confront Sid, a child who tortures and murders toys for his own amusement. This stops the actions of one owner, but leaves innumerable others unwittingly murdering sentient beings on a daily basis.
In the latter two movies, the toys alter their situations in more passive ways, such as escaping from a master they deem illegitimate (Almost always back to their master, not from him, despite knowing it will lead to their eventual abandonment).
Over the course of the series, the protagonist is branded, neglected, tortured, damaged, stolen, put up for sale, helpless to stop the sale of his romantic partner, goes years without human affection, and then is finally given away to a master who is young enough to have a use for him again, assumedly beginning the cycle over again, until he is inevitably too damaged to be of use to humans any longer, and is left to rot in a landfill.
Still not as soul-crushing as The Brave Little Toaster.
As touched on earlier, the relationship between humans and toys would presumably be more equitable if the humans were aware of the toys' sentience. Until the origins of the "rules" are known, it is unclear as to who is at fault for the system of inequality in the first place.
That being said, it is probably not a good idea for humans to know that they have limitless, god-like creative powers. Skynet wouldn't have anything on the endless supply of nightmare fodder churned out by the creepy porcelain doll industry alone.
Then again, living toys could end the current American recession, through bringing manufacturing jobs back to the US-- presumably out of the hands of the other Disney-sponsored slaves that humans like to pretend aren't sentient.
Phenomenal Cosmic Power... Itty Bitty Living Space.