In most Korean songs, gaseum (가슴) and maeum (마음) are translated to heart, but what are their main difference?
가슴 is breast or chest.
마음 is attitude, thinking or feeling.
Sometimes 가슴 can be used to mean 마음 but 마음 cannot substitute 가슴.
I will give you examples to help your understanding.
내 여자친구는 가슴이 커. (My girlfriends has big breasts.)
내 여자친구는 마음이 커. (This usage is incorrect.)
어제 여자친구랑 헤어졌어. 그래서 마음이 아파. (I broke up my girlfriend with yesterday, so I'm heartbroken.)
어제 여자친구랑 헤어졌어. 그래서 가슴이 아파. (가슴 is used to mean 마음.)
그녀는 마음이 참 따뜻해 : She is very kind.(A literal translation would be "She has a warm heart.)
그녀는 가슴이 참 따뜻해. (Her breasts are warm; This sentence is quite weird to me, though. Or it's possible that people would accept 가슴 as meaning of 마음.)
It can be difficult for you because sometimes 가슴 can mean 마음, but 마음 can never replace 가슴.
Do you think the examples look naughty? It's true. 가슴 can have a sexual connotation in normal conversations. (Basically, in Korean 가슴 means both "breast" and "tits.")
Side note : On the internet, 슴가 is a slang of 가슴.
Adding to TING CHOE's great answer,
There are situations when 가슴 and 마음 can both be used to mean heart.
The sino-Korean of 마음 is 심(心), and is related to the word 심정. Therefore 가슴 and 마음 is interchangeable when you want to express your or others' feeling. Situations other than the one abovementioned is normally not allowed to interchange.
Ex: (가슴/마음)이 아프다
But then which one to choose? Really, in 99% situation, it doesn't matter. But I tend to think that native speakers will choose the one which is EASIER TO READ OUT or MORE NATURAL. This is especially true in songs.