Groups are exactly what their name indicates: multiple Items grouped together. However, not just any two (or more) Items can be in the same group. All of the Items in a Group must share at least one command (E.g. On, Dim, Set Temperature, etc.). So you would not be able to group any of your SmartThings lightbulbs with your Insteon sensors since there are no shared commands between these two Items. Beyond that one restriction you can get as creative as possible! If you want to turn on your sprinkler system whenever you turn on your AC, or more practically turn on your bedroom heater whenever you turn on your bedroom light you are free to do so!
You name Groups when you create them. The Group will behave the same as any Item on your Item List, except SimpleCommands will relay your commands to several Items at the same time rather than a single Item.
Even though Items in a Group may not share all of their commands, you are able to utilize any shared commands in the Group.