As a noun, it means a “swear word” or “curse.” In the verb form [욕하다], it can mean “to swear at,” “to curse at,” “to speak ill of,” “to slander,” “to [verbally] abuse,” “to badmouth,” “to revile,” etc.
It’s not that hard to translate the word when it’s in it’s present, affirmative form; the awkwardness comes when you’re using the imperative (i.e. commanding or prohibiting someone to do something.)
For example, I’ve seen 욕해 translated as “curse me,” where “curse” sounds more sorcerous than slanderous. Curse at me would be more accurate but that sounds odd in English. As does “revile me,” “speak ill of me,” “swear at me,” etc. Personally, I’d go for a looser translation and use “hate/despise me” or “scream/shout/yell at me” depending on the context, because the sentiment is the same (i.e. you don’t speak ill of someone to their face unless you (a) dislike them (b) are angry/frustrated.)
욕하지마 presents a similar problem. I’ve usually always seen it translated as “don’t curse me” which makes me cringe (again, it should be “don’t curse at me.”) But I think it’s more natural to say “don’t despise me” (and hence say bad things about me, etc.)
My translations aren’t perfect but it’s taught me one thing: a word in one language does not always equal a word with the same definition in another language. Translation is about capturing the meaning AND the sentiment of the original language. Literal translations are just plain gross, people.