What does it mean to "cycle" a fish tank?

This is the old tradition from Stoke-on-Trent of building a huge glass building (4 miles long by 1.5 miles  wide), filling it with water and koi. And then taking a Dawes, Raleigh or Claude Butler round it. Participants need to wear airtanks and wetsuits.

I think that's right. (or near enough, anyway).

Feminists are fond of saying that a woman needs a man like a fish needs a bicycle. Your question has shown this to be nonsense. How could they cycle a fish tank if they couldn't ride a bike?

it means to cycle a fish.

To cycle a fish tank basically means to establish, cultivate or grow a bacteria colony inside your filter.

http://www.oscarfishlover.com/how-to-cycle-your-aquarium

To cycle a fish tank is to cultivate bacteria to feed on ammonia that is in fish tanks. Despite being arguably the most important step in aquarium starting, it's skipped more often than not. There are multiple methods to doing a cycle. One method is to introduce small amounts of hardy fish that can survive in an uncycled tank for a certain period of time. Over time, more bacteria will be grown and gradually balance out the toxin levels. This method is a bit frowned over since it can damage the fish you use. Another method is to use biological waste in the place of fish such as fish food or parts of other tanks that have been exposed to bacteria. Adding small amounts of ammonia can also help. A quick way to cycle is to buy an instant cycle product that contains bacteria. These can be poured into the tank and instantly cycle it, but there is some speculation over how well these actually work so you might want to start adding small amounts of ammonia beforehand.