When you are browsing through a Private Window with Tor, Maiar doesn’t connect directly to a website but, instead, you connect to a chain of three different computers in the Tor network, one after another, and only then to the website you’re visiting.
Tor is a a network that protects you by bouncing your communications around a distributed network of relays run by volunteers all around the world. It prevents somebody watching your Internet connection from learning what sites you visit, and it prevents the sites you visit from learning your physical location. This set of volunteer relays is called the Tor network.
Individuals use Tor to keep websites from tracking them and their family members, or to connect to news sites, instant messaging services, or the like when these are blocked by their local Internet providers. Tor's onion services let users publish web sites and other services without needing to reveal the location of the site. Individuals also use Tor for socially sensitive communication: chat rooms and web forums for rape and abuse survivors, or people with illnesses.
Journalists use Tor to communicate more safely with whistleblowers and dissidents. Non-governmental organizations (NGOs) use Tor to allow their workers to connect to their home website while they're in a foreign country, without notifying everybody nearby that they're working with that organization.
Groups such as Indymedia recommend Tor for safeguarding their members' online privacy and security. Activist groups like the Electronic Frontier Foundation (EFF) recommend Tor as a mechanism for maintaining civil liberties online.
Corporations use Tor as a safe way to conduct competitive analysis, and to protect sensitive procurement patterns from eavesdroppers. They also use it to replace traditional VPNs, which reveal the exact amount and timing of communication. Which locations have employees working late? Which locations have employees consulting job-hunting websites? Which research divisions are communicating with the company's patent lawyers?
What if I want absolute anonymity while browsing?
Maiar works hard to ensure that you’re extremely difficult to track online. But if your personal safety depends on remaining anonymous you may wish to use the Tor Browser instead.
PS: Note that Tor windows are only available for the Desktop version of the browser at this time.