In plain language it is a simple bicycle without gears.
A single-speed bicycle is a type of bicycle with a single gear ratio. These bicycles are without gears, hub gearing or other methods for varying the gear ratio of the bicycle.
Single Speed bikes include any type of bike with one single gear.
Benefits include a very low maintenance, simple and minimalistic looks and simplicity. They are also lighter than geared bikes due to smaller amour of parts used on them.
Fixed Gear or Fixed Wheel bikes are a type of single speed bikes, however a term Single Speed Bike is usually referred to a normal 1 gear bicycle you can freewill or coast (meaning stop pedalling while still in motion).
There are some single speed bikes completed with a Flip-Flop Hub which takes both - normal single speed and fixed gear sprockets letting you choose which one to ride.
Please also see our articles on Fixed Gear Bike Explained and Flip Flop Hub Explained.