this taxi was coming around the corner ne anlama geliyor?

Bir çeviriye bakın

In informal language you can use “this” even when you’re not talking about something that’s in front of you. It’s a more exciting, if technically incorrect, way to say “a”

Coming around the corner means the taxi driver was turning from one street onto another street - the corner is the part of the block where two streets intersect. My guess is that the person saying this was nearby, probably standing on the sidewalk at that corner, when the taxi turned, and that something interesting happened after that.