A grain of salt...
This is a very short and fast summary. There are plenty of sites on the Internet where one can learn more about Aikido (the way of harmony) but here are some suggestions: The Aikido FAQ is a good place to start, wikipedia should be no surprise, and finally a stackexchange question site exists if you have questions.
Daito-ryu aiki jujutsu 大東流合気柔術
Daito-ryu aiki jujutsu was originally the unarmed combat method of the samurai of the Takeda clan and dates back around 900 years. Its lineage was passed down to Takeda Sokaku in the early 20th century. He decided to pass it onwards to one of his most gifted studen: Morihei Ueshiba.
Ueshiba mastered daito-ryu and started teaching it in the early 1920/1930. However, Ueshiba interest in the Omoto-kyo religion led him to modify a lot of the hard techniques of daito-ryu into something softer and named his style Aikido. During that time, Ueshiba demonstrated his style to Jirogo Kano, the founder of Judo. The latter was so impressed that he sent one of his top students, Kenji Tomiki, to train with Ueshiba. Tomiki joined Ueshiba in the so-called Hell Dojo and was given a certificate of mastery (meiko kaiden) from Ueshiba. The first one ever to be given which was eventually translated into an 8th degree black belt.
Shodokan Aikido 昭道館合気道
After the second world war Aikido, in common with all Japanese martial arts, faced great difficulties. Tomiki focuses his efforts in bringing the art into universities. Tomiki, being a student of Judo, started to incorporate Kano's ideas of martial arts into Aikido. After years of work, Tomiki founded his own style called Shodokan Aikido. This is the style that the York club trains in. Currently, the head of the style is Tetsuro Nariyama, one of Tomiki's top students.
• Aikikai, the organisation founded by Ueshiba.
• Ki Aikido, a soft style founded by Tohei.
• BAB, the UK the Aikido umbrella organisation.
There are too many other styles of Aikido and organisations to mention them all here.