Character groups are just that, groupings of characters. They are used throughout mx in various ways.
Mx can translate character codings to content (similar to Lucid based descriptions). This is done through character groups. Select the characters you'd like to see in a concatenated "description" into a character group. Link that character group to a content type using the "map to content type" field. You'll have to have created content types before hand. You can link more than one character group to a content type. To see all possible text do Character Group->show->content mappings. Text in this view will be linked to the ontology if you have selected one in the projects settings or you have an ontology in the project.
To see the actual generated description for an OTU first create a template and include the content type(s) that you have mapped character groups to. Then do Otu->show->content. From here click "matrix syncing". If you have properly setup the character group to content type mappings you'll see text here. By clicking "update" the action described in this screen will take place, and the codings based description is saved. Note that updating codings *does not* automatically update the description. The intermediate step of copying the matrix based description to raw text allows you to go back and edit the text of the description for clarification, additions etc.