is a line on the terminal
screen, usually on bottom, or similiar thing on a window
on a GUI, that contains some status
For example, status line of this window I'm looking at now has "Document: Done." That's Netscape's informative way of telling that this page has been loaded completely.
Or, the window I'm looking at now has this stuff:
[IrkkuVirveli(tm)] WWWWolf(+i) on #everything(+tnr) [L] [00:39]
This is sirc's status line (with Howl! script).
Unless I'm mistaken, "The Status Line" was also the name of one Infocom magazine - as most Infocom games had a status line like this one:
West of House Score: 0 Moves: 0
(Guess what game?)