When universities announce a large tuition increase and follow it with an announcement that more financial aid will be available, they are assuming that students who pay full tuition have inelastic demand and students who use financial aid have elastic demand.
An elastic demand is one in which the change in quantity demanded due to a change in price is large. An inelastic demand is one in which the change in quantity demanded due to a change in price is small.
A good's price elasticity of demand is a measure of how sensitive the quantity demanded is to its price. When the price rises, quantity demanded falls for almost any good, but it falls more for some than for others.
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