Return values are what is returned to you when you execute a command or procedure.
For example:

{
	string $sphere[] = `sphere`;
	print $sphere;
}

The sphere command returns a string array containing two things.
The name of the sphere and the name of the makeNurbsSphere node.
To get the return value of a command you use this character ` around the command.
You've seen this done with the size command, on the arrays page.

IMPORTANT: the ` character is not the single quote found on the " key.  It is the
one found on the ~ tilde key next to the number keys.

This can result in a lot of frustration if you don't know it, and for some reason it doesn't
seem to be mentioned in the help docs.

The Maya help docs tell you what to expect a command to return, so consult them for specific commands.
They can also return different variable types depending on what flags are used.

Procedures that you create can have return values too. This is covered on the procedures page.