Why is the breton language similar to the welsh language?

The Old Brythonic language was once spoken along most of the west coast of Britain, from Strathclyde (now in south west Scotland) down through Lancashire and what is now Wales and on to the horn of Cornwall. During the Dark Ages and the early middle ages the language disappeared from the Scottish south west and most of Lancashire, and speakers in what is now Wales became separated from the Cornish - so Cornish and Welsh became distinct languages.

At around the same time (from about the ninth century on) a significant number of migrants from the Old Brythonic western littoral migrated to Armorica (the extreme western tip of France) taking a language with them which rapidly became Brezhoneg (Breton).

So Welsh, Cornish, and Breton all began as local dialects of Old Brythonic.

Breton is actually closest to Cornish, but since Cornish is all but dead this similarity is rarely noticed. Welsh is one of the most successful minority languages in Europe, so it is easy for Breton speakers to notice how close their own language is.