Track Groups have a property titled Select which, if enabled, cause Ardour to propagate a region selection in one track of a group to the corresponding regions of the other tracks in that group.
For example, let's assume you have used multiple microphones to record a drum kit to multiple tracks. You have created a track group, added all the drum tracks, enabled the group and enabled the Select property for the group. When you select a region in one of the drum tracks, Ardour will select the corresponding region in every other drum track, which in turn means that a subsequent edit operation will affect all the drum tracks together.
Regions in different tracks are considered to be corresponding for the purposes of sharing selection if they satisfy all the following criteria:
Sometimes, the rules outlined above are too strict to get Ardour to do what you want. Regions may have been trimmed to slightly different lengths, or positioned slightly differently, and this will cause Ardour to not select regions in other grouped tracks.
In this case, change Edit > Preferences > Editor > Regions in active edit groups are edited together: to whenever they overlap in time. With this option enabled, regions in different tracks will be considered equivalent for the purposes of selection if they overlap. This is much more flexible and will cover almost all of the cases that the fixed rules above might make cumbersome.