Ardour has a global edit mode selector at the left of the Editing toolbar, which affect how regions are moved or copied:

Slide
Regions move freely. Ardour creates overlaps when necessary.
Lock
No region motion is permitted (except for "nudge").
Ripple
The effect of an edit is reflected in the regions to the "right" of the edit

More details about Ripple

Ripple Edit mode provides the following conveniences:

If Snap To Grid is enabled, then regions can only move so that they align with locations determined by the current snap settings (beats, or seconds, or other region boundaries, etc). See Snap To the Grid for details.