The critical period is defined as being the “biologically determined period of life when language can be acquired more easily and beyond which time language is increasingly difficult to acquire. ”
The critical period hypothesis is a scientific argument based on biological facts on how the human brain develops and changes over time. Before puberty, the brain has high plasticity—not in the sense that you could mold McDonald's toys out of it, but in that its development is very flexible, with an extraordinary ability to absorb new information and concepts.
After puberty, the hypothesis goes, the brain begins to undergo a process called lateralization, in which certain functions, like language, are assigned to either the left or right hemisphere of the brain, which would make further language acquisition difficult. A good deal of this is theorized to be because people will actually begin to overanalyze any attempts to learn a language, as opposed to learning in an organic and open manner.
As with all things scientific in nature, this hypothesis is up for debate. Does it hold while under scientific scrutiny?
Well, it's not a simple answer, as with most things. There are two main approaches to CPH, an extreme view and a softer view. The extreme view, that after puberty true language acquisition is impossible, has largely been negated. However, a softer view is that language acquisition is merely more difficult and not necessarily impossible. One aspect where CPH has held particularly strong is with regards to phonology in language acquisition; basically the ability to develop a native accent.
There is a lot of interesting research going on right now with regards to CPH. For instance, check out this recent study in which babies are found to cry in their parent's accents by their second day of life. The validity and strength of CPH has been a longstanding debate for decades amongst psycholinguists, and appears set to continue on for a good deal more.