Assemblies are coherent pieces of a project. For example, if you're designing a desk with a hutch, you could treat the desk and the hutch as two separate assemblies.
An assembly consists of one or more components.
Breaking a project down into assemblies makes it easier to design and copy parts of projects for use in future designs. For example, you can make a copy of an assembly and use it or modify it within the same project. If you were, say, designing an office with a number of built-in bookcases, you could design and place the first bookcase, and then clone that bookcase into another location in the project.
However, in general it's best to have as few assemblies as you can logically get away with. A component within an assembly, such as a board, is located in relation to the left-most, front-most, and bottom-most corner of the assembly. The components in one assembly are not directly referenced to components in other assemblies; they are only indirectly referenced through the project. So when you're working with multiple assemblies, placing a component in one assembly relative to a component in a different assembly sometimes requires a bit of calculation to get just right.
An assembly is defined by its name, its overall dimensions, and its location within the project.