Limits repreesent a value of a function that normally is undefined. For example: $$f(x) = \frac{x^2-4}{x-2}$$ You normally can't find f(2) because that would equal \(\frac00\) o\in limits, You aproach the number from the left and the right, and find what f(2) APPROACHES, notice that I said from the left and the right because if it approches a different value from the other side, the function is DISCONTINUIOUS, for example:
$$f(x) = \begin{cases} x^2 & \text{if } x < 2 \\ x + 4 & \text{if } x > 2 \end{cases}$$In this function, there is a hole at x=2, but since it isn't continious, we can't take the \(\lim_{x \to 2} f(x)\).