From Unofficial BOINC Wiki
A Host is another name for a computer system that is running a software application. For example, your computer, running the BOINC Client Software is the Host for the BOINC Client Software and the Science Applications that are attached to it.
Host is just a computer geek way of saying "computer".
Each of the Participant's Computers is considered to be a Host and is assigned a Host ID that uniquely identifies the Host to the Project. The Host ID is a unique integer number that is the Primary Key for the Host Table in the BOINC Database.