From MozillaZine Knowledge Base
This article will concentrate on describing how Private Browsing works and what issues you can encounter if you are in "Private Browsing" mode.
For brevity this article will use PB to refer to "Private Browsing" mode.
If you are in PB mode then any feature that requires storing data to a file on the hard drive is disabled.
This means that Firefox will not use the disk cache but only the memory cache if enabled.
No new history is kept and that also means no indication of visited links. You still have access to history that was kept in previous normal mode sessions.
All cookies created while in PB mode are session cookies that expire if you end that PB mode session.
SeaMonkey has added PB support as an experimental feature with its 2.18 version. Most functions (and any associated caveats and bugs) are the same as for Firefox, except for running PB mode automatically at startup which hasn't been implemented yet.
Check for Private Browsing mode
You are in "Private Browsing" mode if you see (Private Browsing) in the title bar or if you see a "Stop Private Browsing" entry in the Tools menu. If that menu entry is grayed then that means that you run Firefox automatically in "Private Browsing" mode. You enter that automatic state either via Tools -> Options > Privacy > History: Firefox will: "Never Remember History" or via Tools -> Options > Privacy, choose the setting Firefox will: Use custom settings for history -> "Automatically start Firefox in a private browsing session". The commandline switch -private will open a permanent PB session that can't be ended unless you restart Firefox without the -private switch.
This automatic PB change will become effective immediately without closing existing tabs (!) and can be used to swap cookies or clear all the private data that you made in PB mode (toggle twice to stay in PB mode; pref browser.preferences.instantApply) or to visit a website that you do not want to save history or other data (cookies) from. If you leave auto PB mode then Firefox will clear the memory cache and all cookies and start using the disk cache once again and start keeping new history and you have once again access to cookies that were created in normal (non-PB) mode.
If you are in PB mode then some menu items and other features will be disabled or not available.
- Bookmarks created while in PB mode won't get a favicon. If you leave PB mode and use that bookmark then the favicon should appear. (Bug 535811)
- Live Bookmarks (RSS feeds) items that you have visited won't get a favicon to give them a visited state.
In PB mode only the memory cache is used and you can't clear the disk cache as long as you are in PB mode.
- If you use Tools -> Options > Advanced > Network > Offline Storage (Cache): "Clear Now" then only the memory cache will be cleared.
Note: Due to a bug, disk cache entries from Private Browsing mode are not cleared after returning to normal browsing mode, in Firefox 15.0 (Bug 787743). 
- It is not possible to make a permanent exception to accept a certificate in case of an SSL error.
- All cookies are session cookies that expire if the PB session is ended or you close (exit) Firefox.
- You do not have access to cookies that were created and saved in normal mode.
- Cookies are shared between PB windows but not with non-PB ones (see bug 874042 for SeaMonkey)
- If cookies are enabled then new session cookies will be created if you visit a website in PB mode.
- In PB mode you can still make an allow or block exception and existing exceptions are still honored.
- Exceptions that you make in PB mode are retained if you end a PB session.
Menu items grayed
- If "Tools -> Stop Private Browsing" is grayed then you are running Firefox automatically in PB mode. You have to go to "Tools -> Options -> Privacy" to disable PB mode by removing the check mark on Automatically start Firefox in a private browsing session.
- "File -> Import" is grayed, so you can't import Bookmarks and other data.
Offline web content
- Data from offline web applications is not available to a PB window.
- However, the user is still asked whether or not to store offline data a web application wants to save for later use, and permissions are set respectively. (Bug 826865)
- If accepted, the offline data is actually stored even though it remains unavailable to the PB window (but is available to non-PB windows.
- Firefox won't offer to store a new password if you access a website and enter a name and password. You still have access to stored passwords, but Firefox won't autofill the name and password. You need to open the name list with a double click in the name empty field. (Bug 539623)
You can find the permissions (exceptions) for the currently displayed website in "Tools > Page Info > Permissions".
- New exceptions that you make while in PB mode (cookies, images, pop-ups, software) will be kept after leaving PB mode.
- Plugins may maintain their own cookie system (e.g., Local shared objects for Flash content).
- These are usually stored and retrieved regardless of the PB status of the browser window the plugin is running in.
Saved form data
- Firefox won't store new entries, but you have access to entries that were stored in a normal session.
- Firefox won't store or keep site preferences while in PB mode. Currently only the Text and Page Zoom ("View > Zoom") and site-specific download directories fall in that category.
- If you zoom a web page in a tab and open a link in the same or another tab, the zoom is reset to the level that was in effect before entering PB mode. (Bug 539016)
- If you have the same site opened in a PB window and in a regular non-PB window, changing the zoom level in the PB window will also change it in the non-PB window. (Bug 873024)