The base plate is the body of the tremolo, and it carries the two hardened knife edges the whole bridge pivots on.

Those edges are the wear part. On a good trem they stay sharp for years; on a soft one they round off, and once they do the bridge cannot return to the same place twice. You'll notice it as a guitar that comes back close to pitch after a dive but never exactly. Filing them doesn't work — the plate gets replaced.