It is my first time here, but I am confuse about what
is Virtual Appliance.
A Virtual Appliance is a pre-built, pre-installed, pre-configured, possible tweaked application + Operating System all in one. It's much like a hardware appliance, but completely in software.
1. Do I need any host OS to start VMWare (player or
workstation) to run the Virtual Appliance?
If you want to run Player, Server, or Workstation, then yes. They are hosted products and require a host OS.
2. if ESX server can run VM image, can it run
independently without VC ?
Yes. VC makes managing multiple ESX Servers easier (and allows for the advanced functionality such as VMotion, HA, DRS, etc.). But it is not needed to merely run a guest VM.