Groups are different from Blocks. With Blocks, you can manipulate the block as a whole, and that is it. If you need to edit a part of the Block, you have go into the Block Editor and make your changes. This will change every instance of the Block in your file.
With Groups, you can edit the object but it will not change other instances of that Group. Also, note that you cannot share Groups from file to file.
To make a Group, type group at the command line. Then simply fill out the Group Name field and enter a Description. If you do not enter a Description you can always fill this in later. Then hit the New button, select the items you want to Group and hit Enter.
So, what can you do with a Group? You can Grip edit the items individually, or move/copy/scale the Group as a whole. Double clicking the Text in a group will not invoke the Text Editor. You have to start the Text Editor command then select your Text to change it.