1.) The VGA planets game server program, host.exe ("THost") or a replacement such as PHost. This is the program which reads the TRN files, checks the rules, performs all actions, and spits out RST files. The host is often extended with add-ons and wrapped with tools that do mail handling (incoming/outgoing), backups and stuff.
2.) Job title of the person doing the hosting (i.e. supplying the computer, running the host program, etc.).