Lockpicking is one of the skills that Elizabeth has. During her time imprisoned she learned it. Once Booker reaches a locked door or a safe, he can call up and rely on Elizabeth to break the lock for him. Although it has some complexity to it. Regular locks will find Elizabeth’s hairpin enough to break them, tougher locks are going to need special lockpicks. These come in the form of leather pouches. You can look for and loot them from defeated firemen or crow. But you can also buy them from Dollar Bill vending machines which might not be necessary because there are a lot of locks scattered around for free. Booker has the capacity to hold up to 30 lockpicks at the time. The counter is misleading with its three digits.
When unlocking boxes and safes you can get various bonuses – ammunition, cash and etc. To add to that, unlocked doors allow you to progress and move on with the story.