In short: It's a Thunderbird Quick Filter Bar extension.

See this blog post to understand what this extension does in greater detail: http://www.visophyte.org/blog/2010/05/02/thunderbird-quick-filter-bar-extensions-theyre-a-thing/

Implementation Notes that are important:

• This extension was originally developed during the transitional jetpack period when it was supported to use XUL overlays and the jetpack guts.

• It is possible to revisit that halcyon time period by disabling the bootstrap flag in the install.rdf file and making sure we have component/contract lines in our chrome.manifest. Annoyingly it appears cfx generates a new classid every time we run "cfx xpi", so I have just been modifying the produced xpi's harness-options.json and install.rdf to reuse the class id from the chrome.manifest and mark it as not a bootstrap extension.