There are many components to economics that are basic intuition to many, but whose terminology is often foreign to the general public. Elasticity is a phenomenon that often falls in that category.
Generically speaking, elasticity is a measure of sensitivity and responsiveness to changes in some factor.
Take, for example, price elasticity of demand. Assume for a moment that the cost of electricity and water increased significantly. Would you use less? Probably not. As a result, this is said to be “inelastic.” Now assume that the cost of going to a movie theater increased substantially. Would you go less? Probably. That’s thus considered to be “elastic.”
While that’s the notion behind elasticity, there are many more types that measure responsiveness to plenty of other factors. You can also have things such as negative elasticities, which typically come into play with generics and substitute goods.
But overall, the next time you hear someone talk about inelastic demand for goods, you now know that means you’ll expect people to consume about the same even as the price of the good increases.