Fish produce ammonia, and if you don't have good bacteria growing in the filter, the fish can get sick or even die, as ammonia is very poisonous. The bacteria eat the ammonia and make it less toxic.
A 'fishless cycle' means putting ammonia into the water to help those bacteria grow before you add any fish to the tank.
The best source of ammonia is a household cleaner, like Jeyes Kleen Off, which you can buy online; it can be difficult to find in shops. You must make sure you buy the right kind though; one that contains ammonia and water and nothing else.