Shape groups define how your spell is executed. A spell has multiple shape groups, each shape group is represented by one of the brown squares in the Inscription Table. The shape group can be changed by pressing arsmagicalegacy.next_shape_group or arsmagicalegacy.prev_shape_group for the next or the previous shape group, respectively.
If you want to have more than two shape groups, you will need to upgrade your Inscription Table. This can be done by right-clicking it with an upgrade, or by putting it in a crafting field with one.
Upgrades need to be applied consecutively, i.e. level one, then level two, then level three. The Inscription Table will retain upgrades when broken.
Shape groups prove useful if, for example, you want to have two modes on a Heal spell, one for yourself and one for your friends.