Doric is the name of the dialect of Scots spoken in the North East of Scotland.
It is sometimes described as a separate language (from Scots), but linguistically it is more accurate to describe it as a Scots dialect.
Scots, Doric and English are descended from Northern Middle English (a form of English spoken in the fifteenth century).
It is part of the West Germanic language family.
There is an ongoing political and linguistic argument as to whether Scots (and by virtue of their close relationship also Doric), are separate languages, sister languages or dialects of English.
The general consensus seems to be that Scots and English are sister languages. However the issues of identity, language divergence, later convergence, dialects and so on are the subject of heated debate and passion.
In brief, Scots diverged from Middle English (Northen) from the 14th to 16th centuries (with additional influences from Dutch, French, Gaelic and Latin). It has since then become progressively anglicized, in part due to entrenched political power structures.
See the entry Scots for more on this (fascinating topic).