You could potentially have three computers involved in your system, that's why they specify the "Host" computer.

Server: QB Company Data File and the "Host" (This is where you turn Hosting on.)

Computer 1: Workstation for User (No Company File)

Computer 2: Workstation for User (No Company File)

But in your situation, it sounds like you have two computers.  So you have one computer acting as BOTH the Host computer where the Company Data File is located and is used by one of the Users.  The second computer is just used by a User. 

Computer 1: Host and Workstation for User (This is where you turn Hosting on.)

Computer 2: Workstation for User (No Company File)

There is one other VERY IMPORTANT note that I have not seen mentioned here.  It is strongly recommended that you DO NOT use WiFi between the two computers if the second computer is logged into the Company File for long periods.  I have seen situations where someone will occasionally log in from the second computer, make an entry or two and close the file with no issues.  But the type of database used for the QB's file can easily be corrupted (as we've all seen) and a WiFi signal is an easy way to cause corruption. 

The other important note is that in the above I said not to have the Company Data File on the Workstations or Non-Hosting computer.  But that's not to say you can't keep an Uncompressed Copy of the file on the other computer.  Do all the usual Backups that QBs wants to do internally (set to every X times, etc.).  But in addition, every night when everyone is logged out or after you've done massive data entry, copy the folder from the Host machine to the other machine as another Backup. 

If you walk in some morning and the Host computer has died, you can always open your QBs from the second machine in Single User Mode without missing a beat.