(1,5) is a discontinuity, it violates the first condition [that f(a) is defined] because as you can see, the point is just a blank dot, there is nothing there, it is not in the domain. (when we say "is f(a) is defined", we are asking if the graph has a point at f(a), if there is no point there then it isn't defined.
(2,5) is a discontinuity, it violates the third condition, [that the value of f equals the limit of f at a]. This is because you can see the graph has a point at (2,5), but it is separate from the actual graph. So if you were to take the limit of the function when x=2, the limit would be 4 (where the point should be). But it isn't 4, therefore the value of f(x) when x=2 (which is 5), doesn't equal the limit when x=2 (which is 4).
(3,1) is a discontinuity, it violates the second condition, [that the limit of f(x) exists]. In order for a limit to exist, the right hand limit and left hand limit must be the same. But you can see that they are not the same at this point. The left hand limit is 1, whereas the right hand limit is 4.