For a "short" explanation, see
this old post of mine (over at the TWC forum) or for a more general one, see the text of the Bulgarian preview of
the TGC mod (in a spoiler text-box near the end of the first post).
Or, basically, once upon a time there were some Bulgars living to the north of the Caucasus and in modern Ukraine. They eventually formed a large state, which the Byzantines later called "Old Great Bulgaria", but after its founder died, his five sons divided it between themselves. The neighbouring Khazars took advantage and conquered the lands of the oldest brother, while the other four fled to different directions - the second fled north where he created Volga Bulgaria (in modern Russia), the third fled to the Balkans where he created Danubian Bulgaria (the currently existing one), while the fourth and fifth fled first to modern Hungary (at that time - the Avar khaganate) and then dispersed, respectively to modern Macedonia and to modern Italy. The one you're thinking about, Volga Bulgaria, eventually became a great mercantile state (at least until the Mongols invaded), a meeting point of Europe, the Muslim world (VB itself became Muslim around the 9th century) and the Far East. And they were very close to Kievan Rus. One of the Volga Bulgar histories, the Jagfar Tarihi (of disputed authenticity) even claims that Kiev itself was originally created by the Bulgars and then got taken over by the Rus (rather doubtful, but it shows they certainly had close contacts, especially since VB was one of the main opponents of the early eastern Russian principalities).
Also, Bulgars and Bulgarians are different things - Bulgars are the old people from the steppes, while Bulgarians are the Danubian mix of the old Bulgars, the local Slavs and the Balkan locals. Most basically it could be said that this mix became complete around the middle of the 9th century, when Danubian Bulgaria was converted to Christianity and developed its own Slavic liturgies and literature, which eventually spread and greatly influenced the other Slavic Orthodox nations (Serbs and Russians), as well as some others.