Other's gave the more relativistic/geometric explanation, but an easier ELI5 analogy I think is: imagine firing a bullet into the air. It'll fall back to the earth, unless you can shoot it so fast it can get past the gravitational pull back to earth. Imagine doing the same on a larger planet: you'll have to fire that bullet even faster to pass the gravitational pull. Now imagine a light gun, on a "planet" with so much gravity that even that light gun firing a bullet at the speed of light, it still doesn't have enough speed to escape the gravitational pull. Gravity bends the path of light, and while it moves at the same speed throughout, you don't have to slow something down to make it fall back in if you bend it enough.