Infinity is the idea of something that has no end. In our world we don't have anything like it. So we imagine traveling on and on, trying hard to get there, but that is not actually infinity. So don't think like that (it just hurts your brain!). Just think "endless", or "boundless". If there is no reason something should stop, then it is infinite. (...) Even these faraway galaxies can't compete with infinity.
In a sense we all have an inkling of what infinity is. It's something that characterises things that never end. A never-ending Universe, or a never-ending list, like the list of natural numbers 1, 2, 3, 4, .... . No matter how long you count for, you can never reach the end of all numbers, and you can't reach the end of an unending Universe even if you travel in the fastest spaceship. This kind of infinity is what the ancient Greek mathematician Aristotle called a potential infinity: it's definitely there, but you will never actually meet it face-to-face. You just can't get to the end of those never-ending lists or expanses. 
Infinity (∞) is an indefinitely large number. The infinity symbol is a "sideways-8".