Hello Shin, If you describe something as crap, you think that it is wrong or of very poor quality. If you put up with something, you tolerate or accept it, even though you find it unpleasant or unsatisfactory. So 'put up with crap' means tolerating and accepting things ,that you find wrong, unpleasant or unsatisfactory. Example: " He still loves her, although she always lies to him, why should he put up with all this crap?"

More acceptable words are rubbish, garbage, trash or junk. = nonsense = comments, ideas, etc. that you think are stupid or wrong = something that you think is of poor quality 'You’re talking a load of rubbish.' 'He’s talking trash (= nonsense).' 'There’s nothing but junk on the TV.' 'Crap' (taboo) is something someone says that you think is completely wrong or untrue [= rubbish]: 'You don't believe all that crap, do you?' put up with / accept crap (= bad or unfair treatment) = to allow someone to treat you badly

This is not said in formal conversation or writing.

put up with = 大概是忍受的意思 crap = something really bad. You use this phrase when you want to tell people that there is something or perhaps a situation that is really bad which you are finding hard to tolerate. E.g. I have to put up with your crap everyday (我每天得忍受你的胡扯） crap 在這裡基本上就是'屎'的意思,或者更準確的說應該是‘像屎般的XX’。通常是用來比喻難以忍受的東西，事情，別人的胡扯，等等。用法非常廣泛。