The horses of Iceland are a so-called gaited horse breed. This means that most Icelandic horses have two extra gaits to offer besides walk, trot and canter/gallop. All horse breeds have these three natural gaits and can perform them without training. The extra gaits that set the Icelandic horse apart from other breeds are called tölt and flying pace.
Tölt is the unique four-beat lateral gait, that the breed is best known for. The horse’s hind legs should move well under the body and carry more of the weight on the hind end, allowing the front to rise and be free and loose. Tölt is very smooth to ride since there is no suspension between strides, as is the case in trot or canter, and it can be ridden very slow up to a very fast speed, depending on the horse.
The flying pace is the “fifth gear”, offering a two-beat lateral movement with suspension. This gait is ridden very fast, even used for racing and only for short distances, 100-200 metres usually. Not all Icelandic horses can pace, but those that manage all five gaits well are considered the best of the breed.
The extra gaits are natural and new born foals frequently show them right from the start. Most Icelandic horses are five-gaited, meaning they possess all five gaits, while some are considered four-gaited, and lack the flying pace. There is a genetic variation that all gaited horse breeds have in common, which allows them to reach high speeds in a given gait without breaking into canter and gives them the smooth lateral movements. Five-gaited Icelandic horses always have this gene from both parents, as do some of the four-gaited horses. Some only have the gene from one parent, making them a pure four-gaiter who do not offer flying pace.
A very extensive study has been made on the gaits of the Icelandic horse. You can read it here.