Simply stated, it means your back pain is associated with movement. Certain motions make it better or worse.
Mechanical low back pain usually suggests there's a problem with one of the moving parts. Perhaps the disc is damaged from trauma or degeneration. Decreased disc height results in a change in the way the spine moves and increases the load on the joints.
Or there may be arthritic changes in the joints making joint movement slow and painful. The ligaments are also affected by the aging process. Sometimes they get thinner but in some cases they get thicker. Such changes affect the way the joint moves, and again, changes the load through the spine.
Mechanical back pain is sometimes called nonspecific mechanical pain when the exact tissue(s) involved can't be identified.