Exponential time means that something takes a very very very very long time to do - much longer than other things that only take a short time. It's like if you wanted to count to a million - that would take a long time, but it's still possible. But if you wanted to count to a billion, that would take even longer - like maybe years and years of counting!
Exponential time is like that, but even bigger. It's when something takes so long to do that it's not really possible to do it in a reasonable amount of time. So if you wanted to do something that takes exponential time, you would need some really powerful computer or some other way of doing it that's really really smart.
People who study math and computers talk a lot about exponential time because it's a big challenge to know how to do things quickly when they take exponential time. They have to be really creative and come up with clever tricks to make things go faster. But sometimes even the smartest people can't figure out how to do things in less than exponential time, which is why it can be such a hard problem to solve.