This is the 13723rd most frequent Polish word.
podobają
"Podobają" means "they please" or "they are liked."
Here, 'podobają mi się' is used as 'I like' in Polish, where 'mi' is the dative pronoun referring to the person who likes something, and 'się' is part of the verb construction.
Podobają mi się te obrazy.
I like these paintings.
In this question, 'podobają się' is used inquiring about someone's liking or preference, with 'Tobie' specifying the addressed person.
Czy podobają się Tobie te kwiaty?
Do you like these flowers?
Here, 'podobają im się' indicates that 'they' like the specified movies, using 'im' as the pronoun for 'them' in dative case.