I've attached a crude diagram which I made in MS Paint to hopefully help you understand.
Look at all of the points I drew on the diagram. What do they all have in common?
For one, they all lie on the y-axis. They also all have the same x-coordinate: 0.
Think about what would happen if any other number were the x-coordinate: the x-coordinate controls how far left or right the point is, so if it were a positive number, the point would be to the right of the y-axis, and if it were negative, it would be to the left of the y-axis.
This means:
If a point is on the y-axis, its x-coordinate has to be 0, because if it was anything else it would be to the left or right of the y-axis. The y-coordinate, on the other hand, can be anything, because as long as the x-coordinate is 0, the point is guaranteed to be on the y-axis.
