Wire that supports 3 telephone lines, but in a house with 2 or 1, by the look of it. Standard telephone color scheme for twisted pair wiring. Could be serving some other low-voltage function or could be abandoned, but that's what the wire is, so that's probably what it was used for.
Also the box says "WE" which stands for "western electric""Western Electric" which was the manufacturing arm of "Ma Bell" (the old AT&T, when "the phone company" meant them, and nobody else.)