In a related question (Does bathymetry affect ocean topography/height?), the effect of atmospheric pressure on sea level is described as "inverted barometer". What does it mean? How does it get measured?
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
The inverted barometer (IB) is a static (isostatic) response of the oceans to atmospheric pressure. The basic equation is IB = -(change in pressure) / [(seawater density)*(acceleration due to gravity)]
Its an inverse relation i.e. with increase in pressure the sea level goes down and vice versa. In simple terms, 1 mbar decrease in atmospheric pressure with result in 1 cm increase in sea level.