The line at a doorway, and the level at which something changes. Both are places where crossing matters.
Old English þerscwold (a threshold), from þrescan (to thresh, to tread) with a second element no longer certain in sense; the line at a doorway was first the beam trodden underfoot when threshing grain.
The point a value has to reach before whatever sits on the other side of it starts to happen. Nothing here changes gradually; it waits at the line and then simply occurs.