Firefox's Reset feature is a useful addition to the web browser that adds options to reset it to a pristine condition. The idea here is to make it as easy as possible for users to remove all modifications they have made to the browser, without having to go through a lengthy process.
If you are familiar with the browser, you probably know that a simple re-installation of it is usually not enough to resolve issues, as the browser will still load the default user profile of the previous version.
So, instead of having to create a new profile for Firefox, users click on the reset button and that is about it.
A new feature that is making use of the reset functionality of the browser will make its appearance in Firefox 25 Stable (which means that Beta, Aurora and Nightly users can already make use of it).
If you are not using Firefox for at least 60 days, a Reset Firefox button is displayed that provides you with the means to do so.
It looks like you haven't started Firefox in a while. Do you want to clean it up for a fresh, like-new experience? And by the way, welcome back!
The notification is displayed at the bottom of the browser, independent from the tabs that you have open in it. It does not go away, and if you do not want to make use of the reset feature, you may want to click on the x icon at the end of the notification bar to close it down.
If done, most settings will be reset. What remains is the browsing history, bookmarks, saved passwords, the form history and cookies, and if the user wants it, also the windows and tabs of the last session.
So what is the idea behind this? According to Asa Dotzler, it provides returning Firefox users with options to start with a clean new profile. This takes care of "old" browsing data, and incompatibilities if they exist, for instance in form of broken add-ons or profile hacks.
Veteran users know that they can do the same either by creating a new profile, or by using the reset Firefox option on the about:support page of the web browser instead.
The message will be displayed whenever a Firefox profile has not been used for at least 60 days. This means that users who work with multiple profiles may get the message as well. Since it is only displayed once every 60 days per profile, it should not really get too much into the way.
Mozilla may not want to stop here though. Asa suggested to reset Firefox automatically if very old profiles are run, which I personally dislike a lot, as it removes control over the process from the user.