Groups are something that I (really all modelers) rely on heavily in my modeling workflow. A finished character model or environment can contain dozens, or even hundreds of separate polygon objects, so grouping can be used to aid selection, visibility, and object manipulation (translate, scale, rotate).
To demonstrate the usefulness of groups, create three sphere's in your scene and arrange them in a row as I've done in the image above.
Select the three objects and bring up the rotate tool. Try rotating all three spheres at once—is this the result you expected?
By default, the rotate tool rotates each object from its local pivot pointin this case, the center of each sphere. Even though all three spheres are selected, they still retain their own unique pivot points.
Grouping objects allows them to share a single pivot so that you can translate, scale, or rotate them as a group instead of individually.
Select the three spheres and hit Ctrl + g to place the three objects in a group together.
Switch into the rotate tool again and try rotating the spheres. See the difference?
Selecting a group: One of the greatest strengths of grouping is that it let's you automatically select similar objects with one click. To re-select the group of spheres, go into object mode, select a sphere, and press the up arrow to automatically select the entire group.