it is used when we pronounce 불었어 stongly, which usually, I think, gives a fun from the tense sound. 불었어 ㅡmeans that something is swollen./has been swollen. 불(is from 붇다/swell)+었(past tense)+어(ending- just think a tail. imagine a cat without a tail. how strange is it!! now you can know the importance of a tail of a setence)

it's '불었어' exactly. normal form is 붇다, in English, swollen (in the water).