욕을 먹다 (yo-geul meok-da) – get criticised/blamed/sweared at/scolded with vulgarities
You get the idea, this is expressing how the subject of the sentence is receiving hate from someone.
욕 – swear word/criticism/etc…
먹다 – to eat
If you translate the whole phrase 욕을 먹다 literally, you’re “eating swear words”.
If you look at it in this way, it might make more sense because if you were to “eat” swear words, it’s kinda like “receiving” swear words.
Example: 나 실수를 많이 해서 친구들에서 욕을 먹었어.
I made many mistakes so I received a lot of swear words from my friends.
I made many mistakes so my friends screwed me badly.