'끓다' is an intransitive verb which does not need an object of the verb while '끓이다' is a transitive verb which needs an object of the verb. '국이 (subject) 끓다 (intransitive verb).' = The stew boils. '국을(object) 끓이다 (transitive verb).' = Someone boils the stew. (The subject of the verb is omitted.) Here are more similar verbs. '아기가 (subject) 자다 (intransitive verb)' = The baby sleeps. '아기를 (object) 재우다 (transitive verb)' = Someone puts the baby to sleep. (The subject is omitted.) '시간이 (subject) 늦다 (intransitive verb)' = The time(It) is late. '시간을 (object) 늦추다 (transitive verb)' = Someone postpones (delays) the time. (The subject is omitted.) As you can see from the sample phrases, '이', '우', '추' are suffixes that convert the intransitive verbs to transitive verbs.

@kty40809 감사함니다~

What you said makes sense. However the real difference is about who is subject. In 국이 끓다, subject is 국(soup). But in 국을 끓이다, subject is omitted. If hidden subject comes out, it would be like this: (내가) 국을 끓이다 or (그가) 국을 끓이다 etc.