An All mountain board is like an all round board that can be used for all types of riding freestyle, freeriding and riding in powder. These are the most popular type of boards sold due to there versitility. Most begineer riders will get an All mountain board as there first board and most people will have at some point owned an all mountain board.
There are two types of freestyle board jib boards and all mountain freestyle boards, both boards are used for tricks jumps rails etc, Jib boards are very flexaxble and have a twin tip which is where the nose and tail of the board are the same shape. They are excellent for rail riding, buttering, jumps, spinning, riding switch etc. All mountain freestyle boards are stiffer and riden a bit longer than a jib board they are good for backcountry freestyle, larger kickers, pipe riding etc. A park board is just another name for a freestyle board.
Freeride boards are designed for riding and carving at high speeds. They are a directional shape and are usually ridden in one direstion and not rode switch. They are very stable at high speeds due to there stiffness and design, and are excellent in the powder.
Hope this helps, Good luck with the riding.