Plants with mobility are able to walk, slither, or crawl, utilizing motile roots or vines. This does not necessarily imply that the plant has any intelligence. Some more exotic forms of mobility includes:
Divisional Body Segments: The branches, vines, limbs, trunk, stalk, or whatever is appropriate, of the plant are now segmented much like the bodies and legs of an insect. This gives the plant mobility.
Wings/Gasbags: These are parts that allow the plant to slowly fly from one area to another. The rate and direction of travel depends largely on the wind. Certain carnivorous plants use this ability to fly in search of food.