When an offensive, harsh or blunt expression is replaced with a mild, indirect or vague one.
Visual euphemisms exist, too, such as the one used for Akiyama Mio's accidental Pantyshot in the K-On! anime (a striped bowl of rice) or when Swastika or the Hammer And Sickle are replaced with more innocuous symbols to avoid offending the audience and/or so the work won't run afoul of laws banning the public display of either symbols.
An orthographic euphemism is spelling a word deliberately wrong (e.g. "porn" becomes "pr0n", "n0rp" or "prawn") to circumvent censorship algorithms on the usenet, websites, social media apps, etc.