Let's take a boat ride on down a river in Canada, shall we? We were told that on Saint John river there is a bridge before the river mouth and under this bridge a ledge makes the waters take various shapes. We can see whitewater rapids, waves and even whirlpools forming. [1, 3] A pretty cool experience, right? So, let's hop on that boat of ours and sail away...
While on the boat, we are chilling and admiring at the view, anxious to flow under the bridge. We are not too far from it, we can see it in the distance, but something strange seems to happen. All of a sudden the boat immobilizes, as if someone closed the tap and there is no more water running in the river. We stay there looking at each other in wonder and after about 20 minutes more or less the boat slightly starts to move again only it does not flow to the sea anymore but... backwards!
No! That's pretty normal... for this river! You see Saint John river, which flows through the city of Saint John (New Brunswick, Canada) is a very special place where the waters of the river meet with the tides of the Bay of Fundy in a confrontation where the strong man wins!
Enough with the metaphors, please.
Pfff, ok! In plain english: the tides in the Bay of Fundy push the river flow backwards.
The tides of the bay are among the highest in the world (they can raise waters up to 11 meters high). They are also semidiurnal, which means that they follow an almost 12-hour cycle of rise and falls. During low tides, the river flows undisturbed towards the sea. It is the high tides that mess things up. Upon entering the bay, the high tides start flowing upwards. Being squeezed by the narrowing sides of the bay, the high tides meet with the outflowing low tides and form a higher incoming wave. This wave starts travelling opposite the course of the river, pushing it back in huge waves and causing waters to rise up to 11 meters. [1, 2, 3]
Screenshot through: www.google.gr/maps
For a 20-minute period the two forces seem to be neutralized and the waters stand still. But the high tides keep flowing inside the bay, gushing into the river and flowing as far as 130 kilometers inland. Twelve hours later, the high tides begin to lower down until they fall below the river water levels, there is another moment of total balance and tranquility before the low tides retract, allowing the river to flow normally towards the seas again.
Those periods of immobility, when the waters balance and there is no movement, are called slack tides. During a slack tide is the only time when vessels can safely sail across the Reversing Rapids. 
There has also been a tourist attraction on the river that offered tours of the turbulent waters (but not too close to the violent epicenter). Having operated for almost 2 decades, the service was ended in 2013. [1, 2]
The geology of the area
The Reversing Rapids are part of the Stonehammer Geopark. Around the bridge of the Saint John river you can see two ancient geologic terranes joining. A terrane is "a fragment of the earth’s crust formed on, or broken off from, one piece of the earth’s crust (or tectonic plate) and attached or welded to the crust on another plate" (source). South of the bridge you can find Cambrian age rocks of the Caledonia Terrane (542 to 490 million years old). Whereas, at the north there are Precambrian age rocks from the Brookville Terrane. Each terrane gets to keep its distinct geological history, no matter the geological history of the terrane it has been adjusted on. 
The two terranes of the area have both come from the southern hemisphere, but display an age difference of 500 years. Probably, these terranes were "chopped off" a continental mass of the South pole and travelled to the North to become part of the ancient North America. 
The last glacial period (20,000 years ago) changed the shape of the area once more. The river did not follow the same route it does today and there was even a waterfall near the point where the Reversing Rapids phenomenon (which is relatively young, only 3,000 years old) occurs. Riverbed erosion and sea level rising made that waterfall to disappear.