For some functions, the value at a particular point may not be defined.
But it might be interesting to find the function's value when a point is 'reaching' to the point.
e.g. f(x) = y, x not equal to 2
5, x =2
Another example:
f(x) = (x2 -1) / (x-1)
We cannot find the value of this function at x = 1, but we might be interested in finding the value when x approach 1 (from positive and well as negative side).
Note: This is required in derivatives, because we want to find a tangent to a curve which is (f(x+h) - f(x))/f(x) where h approaches to 0. When h is 0, it tangent (or any line) does not make sense (undefined). Thus, we want to find the value of the above expression when h approaches 0.