A limit can be taken from one side at a time. $\lim_{x \to a^-} f(x)$, read aloud: the limit of f of x as x approaches a from the left, uses only inputs smaller than $a$, creeping up on it from below; the small minus sign marks the left side. $\lim_{x \to a^+} f(x)$, from the right, uses only inputs larger than $a$. The two-sided limit $\lim_{x \to a} f(x)$ exists exactly when BOTH one-sided limits exist and are the same number, and then it equals that number. If they disagree, the two-sided limit does not exist; there is no averaging, no tie-break, no side that wins.

A jump is precisely this: two one-sided limits at different heights. The graph has two shelves meeting at $x = a$, one of them with a closed dot. That dot is $f(a)$, and it is as irrelevant to the limits as ever: a jump has no two-sided limit even though the function has a perfectly good value at the jump.