Larceny is basically stealing. Grand larceny is stealing something large or valuable. Petty larceny is stealing something small or of minimal value. Shoplifting is generally regarded as a form of petty larceny. Legally speaking, larceny is defined as the "trespassory taking and carrying away of the personal property of another with intent to legally deprive him therein."
Robbery is basically larceny plus the added element of force or intimidation. So, if I threaten to harm you unless you give me your bracelet, I'm committing a robbery. If I point a gun at the cashier and order her to empty out the cash register, I'm committing an armed robbery. Think about this: If a pickpocket lifts your wallet from your back pocket, that's larceny (it's just stealing with no force or intimidation). But if a mugger approaches you on the street and holds you up at gunpoint and then steals your wallet, that's a robbery.
Burglary involves the element of breaking and entering. You might think of it as larceny plus breaking and entering. When a person breaks into your house and steals the money out of your safe, that person has burglarized your home. At common law, burglary was characterized as the breaking and entering into a dwelling house at night with intent to commit the crime inside, but of course today a criminal can burglarize a business or any other kind of structure, at day or at night.