Alternatively referred to as Private Browsing, InPrivate Browsing, or a Private Window, Incognito mode is an Internet browser setting that prevents browsing history from being stored. Normally, when you visit any web page, any text, pictures, and cookies required by the page are stored locally on your computer. Additionally, any searches or forms that are filled out may be stored in autocomplete fields. Incognito mode forgets this data when you close the browser window, or doesn't store it at all.
How safe is private mode?
Private browsing is not meant as a way to be completely anonymous on the Internet. As mentioned earlier, it is an easy and quick way to not log your browsing history or save (cache) any web pages, images, or cookies as you are browsing. Below are some additional considerations to think about while in private mode.
Other monitoring software
If your computer has monitoring software, like parental controls or keyloggers, they can still capture and monitor everything you are doing, even if you are in private mode. Monitoring can also be done at the network level, which means any school or corporate monitoring that may be running on the network could also capture any private browsing.
Your IP address
Although nothing is stored on your computer in private mode, you are still not anonymous on the Internet. Each page that you visit still recognizes your IP address. If someone had the ability to view your IP address history for legal purposes, an ISP, website, and even a search engine server log could be used to track you.
Add-ons and plugins
Any add-on or plugin you have installed in the browser could be storing information on your browsing habits. For example, early versions of the Adobe Flash plugin allowed cookies to be saved in Adobe Flash even when in private mode.
People standing behind you
It may seem obvious, but anyone shoulder surfing is going to be able to watch what you are viewing in private mode.
Additional security concerns
In the paper "Opening the 'Private Browsing' Data - Acquiring Evidence of Browsing Activities" by Rodrigo Ruiz, it demonstrates getting data from computers browsing in private mode.