It means "almost" or "nearly" :)
is it related to nerede meaning "where"?
Well, yes and no. They definitely come from the same root, but their meanings (at least nowadays) are quite different and aren't really related.
Teşekkür ederim, Alex – but if nerede and neredeyse are not really related, how am I to understand the latter, seeing it for the first time (as far as I remember)? I was absolutely at a loss when I saw it.
Well, an English learner might have the same difficulty with "almond" and "almost", or "bed" and "bedlam". Keep at it -- read a lot, practise a lot.
Why isn't it: bir kahve or kahveyi?
Because it's not ask for one or a specific coffee bir/(-y) -i
why is içiyorsun incorrect ?
“içiyorsun” is the continuous form (“you are drinking”). I think when one does something regularly (“every morning”) you do not use the continuous form.
isn't the meaning of "her" and "hep" the same - every, each??
my answer "Neredeyse hep sabah kahve içersin" was not accepted.
Why " sen her sabah neredeyse kahve içersin " is wrong?