What Each One Is
Both elastic and inelastic demand describe how strongly buyers respond to a price change — the difference is whether that response is large or small relative to the price move itself.
Elastic demand
When demand is elastic, buyers have good alternatives and will switch away if you raise the price. Think of restaurant burgers: if one place raises its price, you can eat somewhere else or cook at home. A 25% price rise can easily cut the quantity sold by 40% or more — the quantity response dwarfs the price move.
Inelastic demand
When demand is inelastic, buyers have no good alternative and keep purchasing even as the price climbs. Gasoline is the standard example: most people need to fill their tank to get to work, and switching to a bicycle is not a realistic short-run option. A 25% price rise might reduce quantity by only 5% — a small response relative to the price move.
The price elasticity of demand (PED) is the percentage change in quantity demanded divided by the percentage change in price. Because demand curves slope downward, a price rise produces a quantity fall, so PED is always a negative number. You compare its magnitude — the absolute value — to 1. When , demand is elastic; when , demand is inelastic; when , demand is unit elastic, meaning the percentage changes are exactly equal and total revenue does not change when the price moves.
For the full formal definition and derivation, see the price elasticity of demand glossary page. If you want a refresher on why quantity demanded falls when price rises in the first place, start with the demand glossary entry.