In most previous math classes, we have learned how to get exact answers. If we want to solve $x^2 - 5x + 6 =0$, the answer isn't "close to 1.99" or "close to 3.01". The quadratic formula tells us: "$x$ is exactly 2 or exactly 3".
In calculus, we have problems where we can't get an exact answer directly. Instead, we find an approximate answer, then a better answer, then an even better answer. The exact answer is the limit of these approximations.
A statement of a limit is "the limit as $x$ approaches (some $x$ value) of the function $f(x)$ is exactly equal to (some $y$ value), which we write as $$\lim_{x \to \tiny\hbox{(some $x$ value)}} f(x) = \hbox{(some $y$ value)}.$$ For example, $$\lim_{x\to 5}(x^2-2)=23.$$