A synecdoche is a commonly used figure of speech whereby a part of something stands in for the whole. We can see an example of a synecdoche at work when we say that a man wants to take a woman's hand in marriage. The man in question, unless he's some kind of crazed psychopath, doesn't just want the lady's hand, he wants all of her; he wants to marry the whole person. The hand, then, a part of the woman, stands for the whole.
In act II, scene IV of King Lear, we are presented with another example of synecdoche. Regan has just suggested to her father that he get rid of half his knights and spend the rest of the month with Goneril, as Regan is away from home and so won't be able to provide her father with the appropriate level of care.
In response, Lear immediately shoots down the idea. He'd much rather “be a comrade with the wolf and the owl” than go and live with Goneril. In other words, he'd much rather live out in the open air like a wild animal than spend a single day under his daughter's roof.
This is an example of synecdoche in that the part—the wolf and the owl—stands for the whole, which in this case is wild animals in general. It says a lot about Lear that he would much rather live out in the open with these wild animals than go and stay with his daughter for the rest of the month.