Morporkian is the language spoken in Ankh-Morpork. It also appears to be spoken to some extent in most other Discworld countries, particularly around the Circle Sea. It is the main language of Lancre, XXXX and most of the Sto Plains countries.
It is remarkably close to Roundworld English, even going so far as to include words like "sandwich", which originate with concepts that don't exist on Discworld. There are, however, a few notable cultural differences. For instance, the expression "as rich as Croesus" becomes "as rich as Creosote" and a popular synonym for insane is "Bursar".
The language is presumably derived from Latatian among other sources. For instance, if we follow the "markers" for the English language and look for their Discworld equivalents, we get Llamedosian = Welsh/Gaelic; Überwaldean = German; Quirmian = French; Hublandish = Scandinavian. And just as Great Britain was founded on maritime trade, Ankh-Morpork, which stands within spitting distance of all these language groups, is a great seaport: words and phrases from languages all over the Disc will have filtered back into Morporkian via a similar sort of mechanism. So its evolution, oddly enough, is not unlike that of English and influenced by similar factors.