You can remember the meaning of 没关系 with this easy mnemonic:
It doesn't matter if you're in a bad mood, it's not (没) okay for you to tell me to shut (关) up. That's no way to talk to your mother, and if that happens again I will tie (系) you up and give you the beating of your lifetime.
Using mnemonics to remember the meaning of Chinese characters like can have an enormous impact on how long to learn Mandarin it takes.