This little guy comes from a webcomic called Gunshow, by KC Green. In the first two panels of strip 648, a character known as Question Hound sits in a burning house, sipping coffee and saying, "This is fine."

The post to the comic creator's page was published on January 9, 2013, and is alternatively titled "On Fire."

The strip, and specifically the first two panels, began circulating on Reddit, Tumblr, and Imgur in 2013 and 2014. Users started to share it to show a situation where they shouldn't pretend everything is okay and under control... and it very clearly isn't.