How does Rebuild in host-raid RAID-1 works?

You are using an Intel Rapid Storage RAID controller. This is not hardware RAID. Like most onboard/motherboard RAID controllers it is host-RAID.

"Volumes with Rebuild status will be rebuilt within the operating system" means exactly that, Rapid Storage relies on a driver within the OS to perform it's work. It is incapable of doing any actual RAID'ing by itself.

Status will be shown using the Intel Rapid Storage console which normally comes bundled with the RAID driver. You're also better off adding/removing/replacing disks using the Windows software and not the very limited BIOS interface.

Depending on your RAID controller the rebuilding should happen as long as you have the machine turned on, but you may need to boot to Windows.

Hardware RAID cards will rebuild automatically, no need to do anything, you don't even need an OS. Many consumer motherboards (Intel Raid etc) it's not real hardware RAID, you may need to boot Windows for the drivers to continue the rebuild (I'm not 100% certain here).

What RAID controller do you have, they usually have their own software that can be used for management/viewing the rebuild process.

I have used various RAID systems (LSI, Intel, Highpoint) and I have never come across one that needs you to do anything to rebuild. Usually just hitting that rebuild option is enough.