The vertical difference between high and low tide in the Bay of Fundy at Burntcoat Head, NS is about 17.0 m during the part of the month when the tidal range is most extreme. That's about the height of a 5 storey building! In places with a near flat beach, the difference between high and low tide points may be a kilometer or more. In a single tidal cycle of just over 12 hours, about 110 billion tons of water flows in and out of the Bay of Fundy. That sounds like a lot. To get a handle on just how much it is, it is equivalent to the combined total 24 hr flow of all the rivers of the world!
What is the science of why the tidal range is so extreme in the Bay of Fundy, while most places the difference between high and low tide is just a meter or so. The most important effect is resonance - the tides are high in the Bay of Fundy because the size of the bay is just right to match the natural gravitational pushing cycle of the Moon that causes the tides.
Imagine you are pushing someone on a swing. The energy of the person on the swing is much more than you give them in any one push, but if you provide the push at just the right time, you keep building up the resonant response. In our case the swing is the flow of water in and out of the bay, and the push is provided by ocean tides caused in turn by the gravitational influence of the Moon mainly (another post will talk about tides in general).
There are two high tides a day, one when the ocean side is nearest the Moon, and one on the side of the Earth most distant from the Moon. This means that the tidal cycle is about 12 hr, but not exactly. That is because in a month the moon makes one orbit around the Earth, and therefore it takes a little more than 12 hr from one high tide to the next (about 12 hr and 25 minutes to be exact).
The Bay of Fundy is just the right length, about 270 km, for a resonance to exist, and we have a high tidal range response (like if you push the swing at just the right time, the person on the swing goes high). If the Bay of Fundy was a bit shorter, or a bit longer, the response would be less.
Many accounts on the web attribute the high tidal range to the shape of the bay. While it is true that the bay gets steadily narrower and shallower, and that helps push the water up, that is very much a secondary effect, with the size of the bay matching the resonant condition being more important. So the shape of the bay helps determine where the tidal range is highest, the fact we have high tides in the Bay of Fundy is primarily due to the size, not shape.
You (or your children) can experience this resonance for yourself in a model bay. Take a long pan with a bit of water in it. Try vibrating the pan with different frequencies (i.e. lift one end up and down in a regular way). If you do it really slowly, the water will just move more or less the amount you push the end of the pan up and down. If you do it really fast, not too much effect. But if you do it at just the right frequency, the sloshing back and forth will build up. And that building up, or resonance, is exactly what happens to create the high tides of the Bay of Fundy. If the bay were shorter, or longer, then there would not be a match, and the tidal range would be much less.
Now while the tidal range is always impressive, exactly how high the range will be is determined by astronomical and other factors. The spring tides (that have nothing to do with the season, but occur during times of full moon and new moon when Earth, Moon and Sun are in a line) will lead to the largest tidal range. Also, the Moon is closer to us sometimes and that will lead to a higher range (but that is a topic for another post!). So enjoy the natural marvel that is the Bay of Fundy!