Englisc, which the term English is derived from, means 'pertaining to the Angles'. In Old English, this word was derived from Angles (one of the Germanic tribes who conquered parts of Great Britain in the 5th century). During the 9th century, all invading Germanic tribes were referred to as Englisc. It has been hypothesised that the Angles acquired their name because their land on the coast of Jutland (now mainland Denmark) resembled a fishhook. Proto-Germanic*anguz also had the meaning of 'narrow', referring to the shallow waters near the coast. That word ultimately goes back to Proto-Indo-European *h₂enǵʰ-, also meaning 'narrow'.
Another theory is that the derivation of 'narrow' is the more likely connection to angling (as in fishing), which itself stems from a Proto-Indo-European (PIE) root meaning bend, angle. The semantic link is the fishing hook, which is curved or bent at an angle. In any case, the Angles may have been called such because they were a fishing people or were originally descended from such, and therefore England would mean 'land of the fishermen', and English would be 'the fishermen's language'.