Wow Michael.
Nice to know you support the little guys. XD
Indie games are games made by Independent developers. This means that the developers aren't working for a big company like Bethesda Softworks, Ubisoft, Bungie, etc. Sometimes they have to use their own money when developing, other times they can raise money or have people back them, like they do on kickstarter.
TL;DR - They are Independent developers who don't rely on other companies.
Avy & Sig credits go to Hurricane0