What is the inverted barometer effect?
In a barometer, you have a tube submerged in a fluid, with a vacuum at the top. If air pressure is low, the fluid can drain out of the tube, letting you read how much lower the air pressure is than some reference value. So, the height of the fluid in the tube goes down as air pressure goes down.

The "inverted barometer" is, in my opinion, much easier to understand.  Over the oceans, high pressure systems push down on the water, lowering sea surface heights a bit. Here, sea surface height goes down as air pressure goes up.  So, it's inverted from a barometer.  But it's really just saying "If I push on something, it'll move" :-p