Tor Browser is a free, privacy-focused web browser that sends traffic through the Tor network. Traffic passes through three random relays, and the last one, the exit relay, forwards it to the public internet. Websites therefore see a Tor connection instead of your IP address, and your internet provider cannot see which sites you visit. The browser is based on Mozilla Firefox ESR, modified to resist tracking and fingerprinting. By default it keeps no browsing history, and cookies are cleared when you exit. You install it as an application on your own device.
Tor Browser is developed by The Tor Project, Inc., a US 501(c)(3) non-profit that, according to Wikipedia, is based in Massachusetts. The software is free and open source. The network is run by volunteers who operate relays, so no central party hosts your traffic. For a European organisation, the relevant points are that it is a locally installed tool whose code can be inspected, and that its developer falls under US jurisdiction.