This is not defined in the manga itself, because Hazama is a known Japanese word, not something that they made up for the story.
Hazama (狭間) doesn't translate perfectly to English, but the closest word we have for it used in that context is Interstice. But, since that is a word that very few people actually know, I can understand why they may not have bothered translating it.
Expanding out to a multi-word translation, we can look at the definition of Interstice. Interstice is a term for the space between two things, particularly when said space is very small.
The other place I found this term in the Berserk manga was all the way back in chapter 114. The Japanese title of the chapter is 魔と人の狭間 (Ma to hito no hazama) translated as "The space between Demon and Man." Here again, hazama carries the implication that the space in question is very small...considering the content of that chapter.
So, when the manga says that Guts lives in the 'World of the Hazama' it is saying that he lives in the 'World Between,' likely referring to the world of humans and the world of demons. To put it in an English phrasing: Guts is standing on the fence between the world of demons and humans.