On the main menu, there are a list of challenges you can attempt. Clicking one starts the game, presumably with differences depending on the challenge.
What is the locked challenge, and what is different about each challenge?
Let's answer with a little help from the wiki. Each challenge is played as Isaac and each one has a specific goal.
There are still things to discover, I'll keep the answer updated as soon as I find them.
Locked challenge is purist, basically do the game without using a single item room. It's pretty hard, since all item rooms are also removed. :P
edit; each challenge adds different things, some are you start with x item, no item rooms allowed, like lord of the flies, others are you're given a handicap, e.g 9 lives where you're stuck with the damn dead cat, but item rooms are aviable, if that makes sense.