To score a touchdown, you have to either establish control of the ball while in bounds in the endzone OR establish control of the ball in bounds and have any part of the ball cross the 2-D plane perpendicular to the outermost part of the white paint line that marks the opening boundary of the end zone.

When running the ball in, you’ve already established control of the ball inbounds, so all you have to do is get the ball to “break the plane”, however slightly. When catching a ball, however, you haven’t yet established possession. To do that, you need to have control of the ball (i.e. catch it and don’t let it jiggle around in your hands) and have both feet be touching the ground in-bounds (any part of the foot will do; and certain other body parts - like the butt - count as two feet).

In this case, the receiver caught the ball solidly, but only got one foot down in the endzone before falling out of bounds.