simply speaking, "왔 is the past form of "오다". the verb "오다" changes as below, base form 오다 past form 왔다 furture form 올것 이다. in your sentence, "오다" is a part of "기다려 오다", and follows the same rule as "오다" base form 기다려 오다 past form or present perfect tense 기다려 왔다. it can mean "to have been waiting" in English. "~ㅆ 다" is one of ways to make verbs past forms. there are some rules to make verbs past forms, as for this, I think you should refer to a grammar. "past forms without '다' + 잖아" is one of difficult expressions to explain, I guess. roughly speaking, it is kinda complaint, and speakers will be upset and annoyed. here are some examples, 가다 갔다 갔 + 잖아 하다 했다 했+잖아

“너만 바라보고 기다려 왔잖아” is meaning do u know I've been waiting for u？？？ 미안해요 제 영어와 한국어는 잘하지 않습니다 maybe "있잖아"+"오"=왔잖아 ㅠ.ㅠ

왔다 is'came' there is an expression '인생여정,-travel of life' people thought that they walked through their life from past to now that is the reason they using 'came -왔다' 너만 보고 기다리며 살아왔쟎아! it will be easy to underStand.