Altium 'Adaptive' Routing
When you select interactive routing and begin routing, press TAB. This will open up the following dialog box.

You'll see Current Mode (under Routing Conflict Resolution). Change that another option such as Push Obstacle. If a track is in your way, it will move the tracks out of the way (so long as it meets your DRC rules).
If you want to manually move a track, you can click and hold, and just move your mouse.