It's a big subject, but here's a starter for 10
For small pressure changes, like you get round aircraft at low speed, air doesn't compress much or change much in density. When greater pressure changes are involved, which come in at speeds over about 300kt TAS or Mach 0.4, the air begins to compress and change density. This gives false readings on the ASI, but equally importantly leads to the formation of shock waves over the wing that affect lift, drag and controlablity
Dick