Burna Boyz are Orks who cannot stop setting things on fire. These lunatics will set light to anything and anyone for the simple joy of watching them "do da burny dance." They can prove utterly lethal to tightly packed or lightly armoured infantry, the roiling blasts of their Burnas flushing their victims out of cover amid the sizzle. Sometimes, if they are rich, some Burna Boyz can one-up themselves with a Splash Burna, a plasma flamethrower hybrid.
Often they join forces with Mekboyz, whom they depend on to supply them with Promethium fuel and the Burna weapons from which they get their name. These dedicated arsonists take great delight in setting fire to the enemy (and anybody and anything else they can lay their hands on if no enemy is available), and it takes a strong Warboss or the blackmailing powers of the Meks to keep them in line. However, the benefits of these lunatics in any Ork warband just about outweigh the risks of getting anywhere near them. The Burna Boyz can be a powerful asset on the battlefield, whether in a small team or large mobs; their mass incendiary firepower can prove devastating, particularly against enemy infantry, flushing out foes from cover and bringing down bestial creatures. Also, with their weapons turned to the searing hot point of a blowtorch flame, they can wield them to hack and slice up enemy armour and vehicles. They serve a vital secondary role in this regard, cutting up battlefield salvage for later use.
Burna Boyz are an elites choice, meaning that they compete for a slot with with Tankbustas, Nobz and Kommandos. As a result most Ork players tend to overlook them as a unit choice -- the Ork codex is and always has been crawling with anti-infantry damage, and Burnas can feel redundant when their slot could be better spent on a different, less overflowing niche. This is not to say that they're bad, they're actually a very good anti-infantry unit, especially in armies revolving around the use of many vehicles. After all, every Burna Boy is armed with a weapon that counts not only as a Flamer in the shooting phase, but also doubles as a Power Weapon in melee depending on the rules for that edition's Assault phase (for example, AP3 in 6th edition).
Versatile Burna - As of 8th edition, it is no longer necessary to choose to use the burna as either a flamer or a CC weapon; you get to do both. As a result, Burna Boyz are not only pretty good at short-range shooting, but are a reasonable threat in melee as well. In 8th Edition, they were kings of Overwatch, and in 9th this is still true: if your opponent has somehow created a situation where you are able to use the Overwatch stratagem on these guys, well, he's either really confident of success or he done messed up- with odds favoring the latter.
Dedicated Transport - Burnas can now take Trukks as a dedicated transport. Remember that when you fire from a vehicle, you can simply find one good placement for the Flamer and have every single Boy shoot with exactly the same angle resulting in dozens of hits on the same unit. Through judicious use of mass tank-shocking (pre-8th edition) or Advancing (8th/9th edition), enemy infantry units can find themselves engaged very quickly, making them prime targets for being purged with fire. A 15-strong mob (assuming you're using a Battlewagon and not a Trukk) has a frightening ability to unleash up to 45 strength 4 attacks which automatically hit. Don't be surprised if your opponent skips saves and just removes the squad. Because of their fragility, having them mount up is probably the best way to get the most utility out of your Burna Boyz.
But then we get to their drawbacks. In addition to the aforementioned Elite slot overcrowding, they are a slow unit heavily reliant on their transports to get anywhere. As soon as their transport is destroyed, the enemy can simply retreat slightly and continue firing at the Burna Boy unit that only has Toughness 4 and a 6+ armour save to protect them. Yeah, Burna Boyz are one of those "expensive gun, fragile soldier" units like Melta Space Marines or Guardsman Veterans, meaning they are almost entirely reliant on transportation and thus mobility to ensure they come anywhere close to proving their worth in an Ork force. This was not helped by the fact that they were themselves very weak to Flamers in certain editions (namely 7th) if they rode in an open-topped Trukk, or their base Initiative 2 if they tried to actually use those fancy melee rules.
8th edition dropped their points to 10 per Burna Boy, for a very good reason: Burnas were nerfed from being exactly as strong as an Imperial Flamer, to half as powerful. A Flamer deals D6 hits, a Burna only D3, a change that was made rather late in 8th edition's development. Based on Mathhammer it's estimated that a Burna costs 4 points to a Flamer's 7. The upside is that a Burna Boy functionally acts as if it had a Power Stabba (S:user, AP:-2) for free, even if they only have 2 attacks base. A lot of players are salty about this nerf, and overall it has made taking Burna Boyz even harder to justify even though they're relatively cost-effective as long as they actually stay alive (see above). Then again, it could be argued that the nerf makes sense since few other armies have a troop selection that squeezes so many Flamers into a single unit.
Regardless of edition, Burnas are generally a tricky unit to use effectively, although cheap 5-man squads with a Trukk in MSU lists can be very effective infantry hunters, backfield objective clearers and even distractions through their reliable damage output against other infantry.