is this a window/wall unit or is the air handler in the attic?
most ac has an overflow cutoff so 1 that may be burnt out or it doesnt have one and 2 it isn't draining the moisture it's pulling from the air so it's gotta go somewhere. don't want to keep it running if it's overflowing like that, the blower motor tends to suck up some of that water and it'll burn out.
the line may be clogged with algea or some small animals like frogs or lizards decided to make it their home and blocked it with debris or their corpse.
first step would be to pour some bleach down the drain pipe if it's got a line draining to outside from the pan to try and kill/clear out some of the shit in the pipe, most stopped up pipes are just clogged with algea. if that doesnt work you'd want to try putting pressure on the line to clear it out.
you can either bring a hose up to the attic and try to force the clog to blow outside or if that doesnt work sometimes it can be easier to backwash the drain with a hose from outside as you can try to get more pressure without hosing down the entire attic but that tends to make a mess by the pan if you dont have someone watching to signal ya to stop when it's flowing.
once you get everything flowing you can get some pan tabs to put in every few months, just slow dissolving chlorine tabs for a/c pans to help keep the drain pipe clear of algea.