Question

what is the definition of limits

Answer 1

"The value a function approaches as the variable approaches some point. If the function is not continuous, the limit could be different from the value of the function at that point."
-Wolfram

Basically, its trying to find what a function is doing at some point of interest. Sometimes, a limit will give you a numerical answer for an equation that by normal routes would be undefined, etc.

Answer 2

@aliaftin limit is defined as the value a function approaches when the independent variable tends or approaches to a particular value.
Let's say we have
\[f(x)=x-2\]
\[\lim_{x\to 2} x-2\]
as x tends to 2, f(x) approaches 0
\[\lim_{x\to 2} 2-2=0\]