Multiple input means the monitor has...multiple source inputs. Most common today are probably LCDs that have both a digital (DVI) and analog input (VGA).
Some more exotic monitors might have even more inputs. For example, the 2405 I'm using right now has 5 (!) inputs - DVI, VGA, S-Video, RCA, and component. The FW900 I have at home supports both VGA and BNC.
It's very convenient for stuff I do, since I run multiple comps so I just use different interfaces for each comp and switch the monitor between them.