Well, I mean, they started off as a HTTP server company with a not lightweight browser, won an antitrust case but lost the war, and reformed as a non profit. Or, well, a for profit company wholly owned by a non profit. At which point they went about rebuilding Netscape suite, the one with mail clients and calendars (and IRC and nntp), as open source software. Then some rogue employees and interns thought 'nobody wants this shit' (https://website-archive.mozilla.org/www.mozilla.org/firefox_...) and firefox was born. Well, phoenix, because engineers never do trademark searches when naming projects. So yea, I don't think anyone fully understands Mozilla, except maybe a few annoyed IRS auditors.
I don't know when Mozilla started taking money for search engine placement, but whoever invented the idea should get a few mil, because now that nobody buys HTTP servers, it's all Netscape/Mozilla has left.
From Google's perspective, it's quite easy to see why they fund chrome: each user that converts to chrome is money they dont have to pay Mozilla. Somehow, despite that depressing metric of user share, mozilla's been making more money every time search bar placement contracts are up for renewal. Some of that was likely competition in search engine space, with both Bing and Yahoo under Marissa chomping for some revenue. I guess the layoffs signal that isn't going to happen again?
Or maybe it signals that you don't need users if your main value anymore is to prove to the DOJ there is no monopoly?