HoMM3 HD is a mod (add-on) for the game Heroes of Might and Magic 3.

This mod is simply invaluable now; I can't even imagine playing Heroes without it anymore.

Added 1 minute ago

Is there an option to disable the selection of the hero arriving at the tavern? Why was this even implemented?

Why would you want to disable it? And if you haven't read the offline introduction, it's mostly for offline tournaments and games. Either way, if you want to order a hero, you do; if you don't, you don't. Consider it as if there's no ordering option, and just play that way.