Grouping objects is a great way to organize your artwork; it gives several objects a common address, so to speak, where Illustrator can find them. After you click any one of them with the Selection tool, you automatically select all the objects in the group.
To create a group of objects, select the objects that you want to include and then choose Object→Group. You won’t see any physical change in the artwork, but from that point onward, all objects in the group are selected at once (provided that you use the regular Selection tool to select them).
The main difference between layers and groups is that grouping organizes objects by their relationships to other objects rather than by their position inside a layer. As any former high-school student can tell you, belonging to a group means having to conform to its rules. Consider these rules, for example:
See Chapter 6 for more information on selecting groups.