How is air pressure related to air circulation?
Air circulation is determined by air pressure.
In order to reach a state of equilibrium (which it never does due to Coriolis effect and unequal heating and humidity), air moves from areas of high pressure to areas of low pressure.
I think this should answer your question but if you want a little more info; Air pressure is affected by heat and water content. Parts of the world are hotter (nearer the equator for example) and parts of the world are drier (Sahara) or wetter (oceans). This sets up the general circulation. Generally air pressure is higher over the equator so generally it is going to circulate away from the equator ( for example).