Contact lenses move differently on eyes depending on their design. All contact lenses are meant to move on the eye to some degree, but how much a lens moves is determined by many different factors.
Type of Lens
Rigid gas permeable lenses tend to move more on the eyes than soft gas permeable lenses. An eye doctor can tell you how much movement is normal for your brand of lenses.
Contact lenses that are too loose might "decenter" and pop out or become caught up in the eyelid. Contacts that are too tight are uncomfortable and might not move at all.
Contact lenses are rinsed and coated in the eye's tears as they are worn, and they are made to "float" on the eye. As a result of this floating a small amount of lens movement as the eye shifts and moves is considered healthy and normal.
Contact lenses are designed to allow movement in order to keep oxygen flowing into all areas of the eye via tears. A contact lens that is too tight and does not move can prevent vital oxygen and moisture from reaching the eye.
Because contacts float on the eye, blinking can cause them to move around. Contacts usually move several millimeters each time a person blinks, and then automatically 'recenter' and float back to the correct position over the pupil.