Megadeth frontman Dave Mustaine explained the song's meaning during Hardradio.com's Shockwave podcast: "'Burn' is, obviously, about fire," he said. "The song is about somebody who's got a questionable past, and rather than doing the obvious, what most people do, lying about it, he just burns it up. There is no proof; there is just a bunch of ashes behind him. And if people try and figure out what this guy is about, they need to sift through the ashes to try and find any proof. I am not an arsonist - I don't condone lighting fires and stuff like that, so I don't want anybody to get the wrong message - but it's basically about somebody who's got a questionable past and is trying to make a new start, but he's doing it in a very questionable way."
Mustaine ended up playing the solo in the middle of the song after he'd done a guide one for guitarist Chris Broderick. The Megadeth frontman explained: "I was gonna show him and I just did it and it's the one we ended up keeping. 'Cause I started playing. I said, 'Just start slow and just keep going faster and faster and faster and faster. At some point, you're gonna double up on the beat so that you're gonna be going against the beat and then you're gonna catch up to it again and then you're gonna pass it.' The solo literally burns during that part; it's just a super, super fast solo. Which is always fun - if you can pull it off and it's clean and it works, it's always great to do stuff like that."
This is one of the few Megadeth songs where Dave Mustaine utters the word "baby" ("burn, baby burn"). He also says it in the 2011 track "Moto Psycho" ("move it or lose it baby"), and to mock the female protagonist in the 1985 Killing Is My Business... track, "Love it to Death."