$\max(0,k-r)$ describes the smallest possible number of blue marbles you draw. Clearly you can't have fewer than $0$ blue marbles, but if there are fewer red marbles available to be drawn in the bag than the number of marbles you draw, you can't have $0$ blue marbles (e.g. if there are two red marbles and you draw 3 marbles, at least one must be blue). So if $k-r$ is positive, $X$ can't be smaller than that.
Consequently whichever is the bigger of $0$ and $k-r$ is the smallest $X$ can be. Now $\max$ is the maximum function, which just returns the biggest of its arguments, so $\max(0,k-r)$ is simply how you express that lower limit mathematically.
For the upper limit, the number of blue marbles you draw cannot exceed the number of marbles you draw, nor the number of blue marbles that are there to be drawn. That is, the most $X$ can be is the smaller of $k$ and $b$, which you write as $\min(k,b)$.