Small business. Computers not on a network. Does Firefox Private browsing keep my boss from seeing my internet activity?
If it is a computer not owned by you or a internet connection not owned by you ... then the owner of either can see your internet activity (domain names and amount of traffic to/from specific IPs if you are using HTTPS).
Firefox Private browsing
... allows you to browse the Internet without saving any information about which sites and pages you’ve visited. [source]
Eg: you dont have to worry about wiping your history ... but any monitoring software on the computer, traffic history on the router, or traffic history provided by the ISP will list all the sites you viewed.
When you launch private browsing in FireFox it literally says:
"Private browsing does not make you anonymous. Your employer or ISP can still see which pages you visit."