Private Browsing Is a Fresh Notebook, Not an Invisibility Cloak
A private window changes what your browser keeps locally. It does not make every observer disappear.
You open a private window to search for a surprise gift. That can help keep the search out of the browser's ordinary local history. It does not make the shopping website forget you signed into your account.
Separate local traces from outside visibility
Firefox's private-browsing guidance distinguishes temporary local browsing data from anonymity. Websites, network administrators and internet providers can still have visibility into activity. Downloads and bookmarks also deserve attention because private mode does not make saved files vanish.

Editorial image from Blogdel's technology collection, used for illustration.
That distinction is useful on a shared computer. Closing the window can remove temporary session data, but the gift receipt you saved to the desktop remains an obvious clue.
Use it for the right task
A private window can provide a separate browsing context or reduce ordinary history left on the device. It is not a reliable way to hide from a service you deliberately log into, and it does not replace account or device security.
Before using it, name your objective: keeping a local search private, testing a fresh session or separating a temporary login. A specific objective makes the feature easier to use correctly. The word private becomes less mysterious once you ask: private from whom, and where?

Editorial image from Blogdel's technology collection, used for illustration.
Sources and further reading
References
- Private Browsing: use Firefox without saving history | Mozilla · primary