They want to build technologies which bring access for everybody. There is a huge population of people who can't type easily and where speech is an important alternative. Having all input running through an ad company (Google) or requiring to buy premium products (Apple) isn't good for an inclusive society valuing privacy.
Quoting their mission statement:
"Our mission is to ensure the Internet is a global public resource, open and accessible to all. An Internet that truly puts people first, where individuals can shape their own experience and are empowered, safe and independent."
https://www.mozilla.org/en-US/mission/
However Mozilla seems like it did too many wrong bets and didn't execute well (see also FirefoxOS)
Quoting their mission statement: "Our mission is to ensure the Internet is a global public resource, open and accessible to all. An Internet that truly puts people first, where individuals can shape their own experience and are empowered, safe and independent." https://www.mozilla.org/en-US/mission/
However Mozilla seems like it did too many wrong bets and didn't execute well (see also FirefoxOS)