Details are not available yet.
The idea is that a Beta version (initial play test game is the Alpha) , which is a nearly completed version of the game, is released to the general public for a limited time. Ostensibly the idea is for players to play the game and provide feedback, but usually the bigger mission for the Devs is marketing. Usually the Betas claim to be by invite only, but the past few Betas have opened up to the public after the first few days.
Call of Duty Betas are usually centered only around the Multiplayer. They have a limited map selection, two or three maps (sometimes a map is added during the Beta) and only a few modes. Players are usually given a level cap, which again is often raised during the Beta. During the Beta, they ask players to take Surveys about the experience.
As I said, it is typically mostly for Marketing purposes, but history has shown that feedback can cause the devs to make changes to the game before the final release. The Betas are also used to stress test servers before mass release.