What does "This was clearly her day off?" mean? Is this offensive to the person, or is it simply stating something obvious?
This question came from Area 51, but I am curious to know this.
This is/was clearly X.
Simply means that the circumstances make it apparent to the observer that X is true.
Without knowing the full context of the statement, I can only speculate, but lets imagine a passage such as:
She woke up at 10:30am, took a long shower, then made coffee, and sat on the sofa to read a magazine. This was clearly her day off.
One can see from the circumstances that the woman is in no hurry to get to work, or other commitments so this was clearly her day off.
The key is the word clearly, which has several synonyms in this context, such as obviously or apparently...
This was obviously her day off.
This was apparently her day off.
Or even some similar phrases:
This seemed to be her day off.
It looked like this was her day off.
Literally, a "day off" means a day that someone isn't at work doing work duties.
However, it can be used metaphorically to mean that someone wasn't working very hard, or effectively, that day. If a tennis player lost every set of a match, a commentator might say "This was clearly her day off". In this context, "off day" (as mentioned by Hellion in a comment on Tom Au's answer) would have a similar meaning, but "day off" would still be a valid expression.