Your employer has the ability (although they are not necessarily implementing the ability) to log network traffic.
So, if you refresh your browser or visit a site while on your company network, the url can and often is logged. Less likely, but possible is that the data contained in those packets is being captured as well. If it’s unencrypted it can be read with any packet analyzer. (Be wary of inputting data in any site that does not start with https://)
Your browser history?
If your browser history is not syncing with any cloud service (iCloud, Chrome, Firefox etc) then it probably safe. It’s not going across the wire, so it can’t be captured.
Even if it is, many cloud services encrypt data syncs.
Firefox does too.