Well, you don't (tell someone what infinity is)

Because you can only tell someone what you do understand. And understanding does not mean that you tell again what you have heard. That, would be an echo of the past. You're not that, you're not an echo. A wall is making an echo. You're not a wall, you are alive so you're much more than an echo.

So what you have to do to really answer anyone, is to understand what you talk about. And the one and only way to understand something, is to discover it, to invent it, so you have to be it. You have to be what you say, you have to let it become part of your bones.

And then and only, you will be able to find a way to present the idea in a way the requester will understand.

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In Maths right now, infinity is not a number, so it's not “a number that goes on always”. Infinity is a limit.

f=1/x when “x” moves very few towards zero, moves “f” very much “towards infinity”. Another way to put it is to say that at a certain point when a limit converges to a value, we can assign that value for this limit (but note that the value of the function and the value of the limit are two different things, even if when the limit converges they both happen to take the same value). When the limit doesn't converge we say the limit diverges, and we write “infinity” which is another way to write “no value”.

So what's the size of the universe? Right now in science we kind of think that the universe “is infinite”, which just happen to mean that it “has no size”…