Taken from Naver dictionary:
1. (입속에) keep[hold] sth in one's mouth
물을 머금다
keep[hold] water in one's mouth.
2. (눈물을)
그녀는 두 눈 가득 눈물을 머금고 있었다
Her eyes were filled with tears.
나는 눈물을 머금고 그를 떠나보내야 했다
I had to hold back my tears and let him go.
3. (미소·냉소 등을)
그녀는 얼굴에 환한 미소를 머금고 있었다
Her face wore a radiant smile.
4.(이슬 등을)
꽃들이 아침 이슬을 머금고 있었다
The flowers were wet with morning dews.
So I think from these examples and definition, you can see it's used when describing something that holds water. Flowers, eyes, mouth etc. This is most common when talking about tears in my opinion. My Korean friends very rarely use this word. But if you were watching a drama and you got choked up, you would be holding back your tears (maybe), so I think it's good for describing this feeling. Or someone that smiles a lot, or puts on a smile even though they are sad, so they have to HOLD a smile.
Hope this helps!