Dago is a slur used to describe Italians in a derogatory way. Slang for Italian, originally coming from Spain. "Diego" was a common name in Italy at the time this slang was first used. See: Wop.
The word Dago is a racial slur that has been used historically to degrade and dehumanize italians. The word is still used by some people for this purpose, and it is seen as offensive and hurtful to italians. If you are unsure about whether or not it is appropriate to use the word Dago, it is best to err on the side of caution and avoid using it in any situation.