Status line is a line on the terminal screen, usually on bottom, or similiar thing on a window on a GUI, that contains some status-related information.

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?)