An offhand remark is something someone says without much thought or preparation.
When people talk about being offhand, they often mean that they were speaking without really thinking things through. For example, if a friend mentions your new haircut and you respond with "Oh, yeah, I just hacked it myself this morning," what you said wasn't very well planned out - the comment was more an easy response than anything thoughtful or considered.
Being offhand can happen in other ways too: maybe someone's remark is blunt or tactless because they weren't thinking carefully about how their words would affect others, or maybe a person says something they don't really mean just to see what happens.
Without planning or thinking ahead.
Example: She gave an offhand speech.
