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:

Deleting a range will move later regions to compensate for the deleted time
Deleting a region will move later regions to compensate for the deleted region's length
Moving a region will move later regions to compensate for the length of the move
Inserting a new region (via dragging or via Paste) will move later regions to the right to compensate

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.