The browser is the application that connects to the world wide web from your computer/device. It works with DNS and HTTP to fetch websites and read the HTML, CSS, code and other content for the browser to display.
In short, the browser has several privacy holes for you to be tracked, identified, and ultimately social engineered through advertising or hacked by bad people. Health companies track your queries when you search on your medical symptoms. The list goes on and on.
But you can defend yourself with some knowledge, tools and best practices. A good start is to read this overview on browsing securely and privately
Advertisers track you across websites and collect your clicks
Ad trackers build a profile of your online habits
Plain HTTP websites leaves your communications unencrypted
Private tabs do not protect your information from your employer or ISP!