Simian is correct. When the slide is in battery and ready to fire, the top of the disconnector fits into the crescent shaped cutout in the slide. If the slide is not closed completely, the disconnector is pushed down, and it disengages the sear mechanism, and the gun can't fire. This link shows the disconnector in operation. It is the vertical piece that moves up and down by the sear. www.m1911.org/images/searanim.gif
More importantly the disconnector "Disconnects" the trigger from the sear allowing the sear to capture the hammer as the slide closes. Next time you have the slide off the frame lower the hammer (DO NOT allow it to drop under mainspring pressure and impact the frame!) and then pull the trigger and attempt to cock the hammer. Be prepared to maintain control of it as the disconnector will not allow the sear to capture the hammer. Keeping the trigger pulled push down on the disconnector with your thumbnail or something none marring but hard. You should feel the disconncect. You can now lower the hammer and the sear will capture it. Then you can release the trigger and you will feel the trigger reset as the disconnector slides back up behind the sear.
This should be one of the function checks you are doing after cleaning and is manditory after a detail strip.