As others have said, in general you use @synthesize to have the compiler generate the getters and/ or settings for you, and @dynamic if you are going to write them yourself.
There is another subtlety not yet mentioned: @synthesize will let you provide an implementation yourself, of either a getter or a setter. This is useful if you only want to implement the getter for some extra logic, but let the compiler generate the setter (which, for objects, is usually a bit more complex to write yourself).
However, if you do write an implementation for a @synthesize'd accessor it must still be backed by a real field (e.g., if you write -(int) getFoo();
you must have an int foo;
field). If the value is being produce by something else (e.g. calculated from other fields) then you have to use @dynamic.