At first, I've learned that yoroshiku means nice to meet you. But then I saw it used in different cases with different meanings. So what are these meanings?
よろしく comes from the word 宜しい, which means good or acceptable, and came to be used to express consent or convenience of the listener. As such, a rough translation might be "if you find it acceptable" or "if it is convenient for you ". For example, 「よろしくお願いします」 might, outside its use as a greeting, be translated as "I would like to make this request if you find it tolerable".