The Moon pulls on the ocean, so the water rises on the side facing it. That much is intuitive and it is roughly right. It also predicts one high tide a day, and most coastlines get two.
The second high tide happens on the side of the Earth pointing directly away from the Moon, which is the part that needs explaining.
It is the difference in pull that matters
Gravity weakens with distance. The Earth is about 12,700 kilometres across, so the near side is meaningfully closer to the Moon than the far side, and is pulled slightly harder.
Consider three things: the ocean on the near side, the solid Earth as a whole, and the ocean on the far side. The Moon pulls all three, but by different amounts. The near ocean is pulled hardest, the Earth’s centre next, and the far ocean least.
Now take the Earth’s centre as your reference point, since that is what the whole planet moves with. Relative to it, the near ocean is being pulled forward, towards the Moon. And the far ocean, pulled less strongly than the Earth’s centre, gets left behind: relative to the Earth, it moves outward, away from the Moon.
So you get a bulge on each side. Not because anything pushes the far side, but because the Earth is pulled out from under it.
This difference in gravitational pull across an extended body is called the tidal force, and it turns up throughout astronomy. It is the same effect that stretched the Moon slightly and eventually locked its rotation, described in why the Moon always shows us the same face.
The Earth turns through both
The two bulges stay roughly lined up with the Moon while the Earth rotates underneath them. Any point on a coast therefore passes through a bulge, then a low, then the other bulge, then another low, in the course of one rotation relative to the Moon.
Two highs and two lows a day. Not because the water sloshes back and forth, but because the coast is moving through a standing pattern.
Why the tide is late every day
Anyone who has spent a week by the sea notices that high tide slips later each day by roughly three quarters of an hour.
The reason is that the Moon has moved. The Earth takes about 24 hours to rotate once relative to the Sun, but in that time the Moon has travelled onward in its orbit, so the Earth must turn a little further to bring the same point back under it. That extra turn takes about 50 minutes, making the lunar day roughly 24 hours and 50 minutes, and the tides keep to the lunar day rather than the solar one.
Spring tides and neap tides
The Sun raises tides too. It is enormously more massive than the Moon but also enormously further away, and because tidal force depends on the difference in pull across the Earth rather than the total, distance matters more here than mass. The Sun’s tidal effect works out at roughly half the Moon’s.
When the Sun, Earth and Moon are in line, at new moon and full moon, the two effects reinforce and the tidal range is at its largest. These are spring tides, and the name has nothing to do with the season; it is spring in the sense of leaping up.
When the Moon is at a quarter phase, the Sun is pulling at right angles to it, the two partly cancel, and the range is at its smallest. Those are neap tides. The cycle between them runs about two weeks.
Then geography rewrites all of it
Everything above describes an idealised Earth covered by a uniform ocean. The real planet has continents, and they break the ocean into basins that each respond in their own way.
Water in a basin sloshes at a natural period set by its size and depth. Where that period is close to the tidal period, the tide is amplified, sometimes dramatically. The Bay of Fundy is the standard example, with a range of many metres, produced by a basin that happens to resonate with the tide and a bay that narrows and funnels the water. Mont Saint-Michel, with its famous expanse of exposed sand at low water, is another.
At the other extreme, a nearly enclosed sea like the Mediterranean has very little tidal range, because it is too small to develop much of one and its connection to the Atlantic is narrow.
And in some basins the geometry favours one cycle a day over two. Parts of the Gulf of Mexico and of Southeast Asia have a single daily high tide, which is not a failure of the two-bulge explanation so much as a reminder that the explanation describes the driving force and not the response.
This is why tide tables are computed locally and why they are indispensable. The astronomy sets the rhythm; the coastline decides what actually arrives.
Related
The same tidal force, acting over hundreds of millions of years, is what produced the Moon we always see one side of. For another property of the sea that turns out to have a simple cause, why the sea is salty.
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