There are many devices and web browsers that you can use to access web resources. Mozilla wants to push the Internet towards full compatibility with all of those devices and browsers, so that users do not run into any issues when they access services and web pages regardless of device or software they use.
That's the main idea behind Webcompat, a new bug tracking service that Mozilla created to improve compatibility on the Internet.
While it has been created by Mozilla, it is not associated with Firefox or other Mozilla products, and Mozilla is not providing resources at the time of writing to resolve reported bugs.
The idea is to make this a web project that Internet users can join to report bugs, or to reach out to websites and services to inform them about them.
As a webmaster, it may pay to visit the Webcompat website from time to time to make sure that your sites and services are not listed here, or if they are listed, to address the issues described in the bug report.
To report a bug you need to have a Github account. That is the only requirement though.
A bug report always includes a web address and a short problem description in five words or less. You can additionally add the browser and version that you used while you ran into the problem, and replication steps before you hit the report bug button.
While you do not have to fill out the optional fields, it is likely that it will increase the chance of the bug being reported to the operators of the site or discussed in the bug report listing if you do.
Mozilla runs Bugzilla that is being used to track issues in products such as Firefox. This includes desktop and mobile web compatibility issues which are handled by the company's web compatibility team.
The Webcompat service on the other hand is vendor-agnostic. It is a broader approach that looks beyond Firefox to ultimately ensure that the web works for everyone regardless of web browser used.
The idea to move the project into the hands of the community is without doubt an interesting one and in my opinion the only logical option.
Mozilla does not have the resources to handle these bug reports on its own, and while the organization keeps an oversight on the project, it is the community that is reporting bugs and contacting website operators to get those issues resolved.
While it has been possible before, the Webcompat service standardizes the reporting and provides the option to discuss reported bugs.
These two links list the desktop and mobile compatibility issues that have been reported using the service. Note that they link to Bugzilla.
The project is at its beginning. This becomes obvious when you open the main website, as the tracking is currently hosted on a dev subdomain which provides you with an early preview of what is to come in the future.
Success or failure depends largely on how fast Mozilla will move the service to the main domain, and word of mouth. If enough users get involved early on, it is likely that it will take off and that it will receive a steady stream of bug submissions for years to come. (via Sören)