Limits are the concept that adding or subtracting an INFINITE number of smaller and smaller numbers can, in many cases, lead to a definite concrete definite result. Similar to the old 0.999999999999.... = 1 argument. Limits are the underlying foundation of all of calculus.
It's the old half the distance half the distance half the distance joke.
Actually, no, the joke goes more like this:
A scientist, a mathematician, and an engineer are each taken separately, in turns, into a room. In this room, a researcher says that once per minute, the participant will cross half the distance to a gorgeous woman standing at the other side of the room.
The scientist and the mathematician both say they're not doing it, and leave, protesting that they'll never get there.
The engineer grins, and says, "okay!"
The researcher replies, "but you'll never get to where she's standing."
The engineer answers, "but I'll be close enough for all practical purposes."