It is called special because of the unique historical and cultural bonds of kinship that unite the American and British peoples through a perceived shared heritage, common political/social/economic values and language. Together over the course of 72 years it has been the White House with the support of 10 Downing Street as its principal strategic leading ally in Europe.
The so-called 'Special Relationship' is an unprecedented coming together and sharing of two nation states intelligence and national security infrastructures and spy-intelligence organisations. The US-UK relationship is highly integrated at an intelligence, defence, foreign policy and security level. As well as being two highly developed, mature, sophisticated economies that do a tremendous amount of trade and investment with each other there are cultural affinities with a shared language and common ancestry.