Questions on Central Air Units

I would like a reality check on a few things that I'm seeing with my central air unit.  I've been doing a lot of reading this morning to try and educate myself better. Recently the unit was running and I found water was draining onto the floor next to the furnace, so I stuck a tub under it and noted that a clear line coming from a small blue unit did have condensation running through it.  The next day I found my little tub was about half full and I drained it and stuck it back.   The next week or so it was cooler outside so we really didn't run it much.  Fast forward to yesterday.

So yesterday the unit was running, and it would shutoff on it's own regularly, and my husband thought it was the power company that was doing that (we get a discount for them to shut off those units if the grid is getting overloaded - it's called Cool Credits. 

What I'm not seeing is water in the tub, nor moisture running in those clear lines.  The house is still cooling, but I'm concerned there's no water.  Is that normal?  And what is that blue unit? 

My thanks to those who can relieve me of this worry.

Almost every time an air conditioner runs, the cold created to cool the air will cause the humidity in the warm air to condense into water as the air temperature is lowered. 

The part of the furnace that gets cold (the AC coils) when the AC is running is tipped, in its mounting, so that the condensed water forms little drops that run to the side and are routed out of the furnace.  The water is routed inside a pipe or tube to a small reservoir on the side of an electric pump.  When the reservoir is full, a float turns on the switch that runs the pump which pushes the water to a remote drain.  Sometimes there is a floor drain close to the furnace and there is no "condensate pump", rather, the condensate lines empty directly into the floor drain.

In your case, the "blue unit" may be a  condensate pump.

The puddle of water on the floor at the furnace indicates that the condensate lines may be plugged, or that the condensate pump may be malfunctioning.  As the condensate runs, it can collect dust from the air passing thru the AC coils, and the dust can build up and block the drain lines or cause the condensate pump float to "hang."  As the AC runs, more condensate water is created, and, in the worst case, the water will overflow the plugged lines and run down inside the furnace itself.

I know the theory, but, as an electrician, I don't regularly service the condensate lines, so I turn to other contributors to suggest DIY condensate system service methods.