Capacity is the maximum possible population that your Empire can support. You increase Capacity by building Housing

Your Tax rate is based on both Capacity and Happiness, whichever is lower. So you need to increase Capacity and Happiness in roughly the same amounts.

Having more Capacity than Happiness doesn't really effect the game other than the "face" icon in the upper left will frown. (If Capacity == Happiness, you also get the frown)

As of June 2010 there are reported problems from users trying to have 50,000 population or more, so this is not recommended.