You unlock them at a certain level. Imagine they're kill streaks type things. When you die (maybe when you're alive, not sure), you can hit B and select one of the 3 possible burn cards you selected before the match. You will then spawn with this benefit. Some are just upgraded dmg versions of guns, some are free Titanfalls, some are Titanfall cooldown reduction (40 secs), faster runspeed, etc etc. You get them based on the challenges you complete in games. Once you die you lose this ability. Only one burn card can be activated at once. When you kill some one with one activated you'll see the 'burncard stopped' or whatever it says.