It’s easy to fool yourself into thinking that the moon is bigger when it’s full, and that it therefore pulls on the oceans more strongly to make higher tides.
But the moon is always the same size and distance away as it circles Earth. It is just lit up differently by the sun at different times in its journey. That’s why it looks to us like a whole disk (a full moon), a partial disk (a semicircle or a crescent) or no disk at all (a new moon). In other words, it goes through phases.
When the moon, sun and Earth happen to be all lined up, we see either a full moon or a new moon. The moon looks full when Earth is in the middle, between the moon and the sun. Think of it as if we are sitting in Theater Earth, with the Man in the Moon on the stage and Spotlight Sun behind us.
We’ll see the full face of the Man in the Moon. On the other hand, when the moon circles around behind us Earthlings, getting between us and the Spotlight Sun (turn around in your theater seat and look at the moon behind you) we see the moon as a darkened disk, that is, a new moon.
In either of these lined-up arrangements, full moon or new moon, the sun’s and moon’s gravitational forces are pulling along the same line of direction, and they reinforce each other to produce an extra-high tide: a “spring tide.”
The name has nothing to do with the spring season; it’s called that because it “springs up” twice in every moon cycle: about every two weeks.