My Cricket stores all the personal acheivements and saved stuff that you acquire during the game as well as edit your options.You can view stats,load your saved games,replays and stuff,and also do a few other stuff in there.If I remember properly the created players are also stored in there.So basically its just a management area for you game.Try playing around and finding what each thing does in there and you should get a fair idea.
If you play other EA games such as FIFA,its analogy is similar to My Fifa... that are in the Fifa games.