A private window is useful, but its name can suggest a larger promise than the feature makes. The first question is not “Am I private?” It is “Private from whom, and which information am I trying to keep separate?”
Think about the browser session
In Firefox, private browsing keeps session history out of the normal browsing history and uses temporary cookies separate from regular windows. Mozilla’s documentation also makes the limits clear: it does not make you anonymous online, and downloaded files or newly created bookmarks can remain after the session ends.
That distinction matters on a shared computer. Closing a window is not the same as removing a document you downloaded to the desktop. Check the actual file location if your concern is what another person using the device can open.
A familiar example: checking a public page
Suppose you want to see how your website appears when you are not signed in. A private window can provide a separate browser session. If you then sign into your account inside that window, you have changed the test: the site can associate that activity with the account again.
Write down the question before testing. “Does this page show the public menu when logged out?” is narrower and easier to answer than “Does this look the same for everybody?” Language, location and other conditions may still differ.
Choose the feature for the task
Use private browsing when session separation or reduced local browsing history suits your purpose. Do not treat the icon as evidence that a website is trustworthy or that a network cannot observe relevant connection information.
If your real problem is an old version of a page, compare the result carefully with how cached copies work. A fresh session can be a useful clue without proving which layer caused the problem.