A batter is basically a mixture of flour and liquid with a pouring consistency. For most pancakes and crêpes eggs are vital to add richness, flavour and air for a slightly risen texture. Add melted butter for even more richness. Water makes the batter lighter and milk makes it smoother.
Mixing flour with water and a little oil and folding in a stiffly whisked egg white makes a very light, crisp coating batter for deep-frying vegetables. For a richer coating batter the egg yolk can be mixed into the flour and water or milk first. Using lager or beer instead of the water in a Yorkshire pudding batter not only makes the pudding rise more dramatically but also adds extra crispness and some subtle flavour, too.