Is my furnace leaking water?
In a comment you said, 


  AC unit is outside.


Assuming you're talking about a whole-house AC unit, what's outside is the condenser. There's another half to the system - the evaporator. it sits inside your "furnace" and cools the air forced over it by the circulation fan in your furnace, which in turn circulates through your ducts and cools your house.

AC evaporators tend to collect significant condensation, to the point that furnaces with AC fitted will always have a condensate pump to collect and dispose of the condensation. You said you mopped up about 8 gallons of water - where I live, that would be a fairly typical volume for a few days of cooling in a typical home. In other words, it's not really that much.

As mentioned by comments, the white box on the side of your furnace is the condensate pump. The hard white plastic plumbing going into the top of the pump is the drain line, which drains the condensate from the evaporator coils into the pump. The pump has a switch inside it that turns on as it fills with water, and the water is pumped out through the smaller-diameter translucent hose coming out the top of the pump. A good place to start troubleshooting this problem is to pour water in one of the empty holes on the top of the unit, and see if it runs and empties itself out.

If it does not run, make sure it's plugged in and has power. If it is, the pump or the switch inside it may be dead. It's not expensive to replace a condensate pump.

Condensate pumps have a check valve on the fitting for the output line, it's possible the check valve is full of debris or clogged and causing the pump to overflow even if it's running. So check that as well, if you can't troubleshoot otherwise.

If the pump is clean and functional, you may have a problem inside your furnace - the tray that collects condensate from the evaporator coil may be damaged (rusted, or there may be debris collected on it that's causing it to overflow instead of properly drain. If you're not comfortable opening the furnace up to check for these problems, it may be time to call a professional.