BM's or Burst Mode ( or Blast Mode in impmon's case) are like megas on steroids, all of the stats are greatly increased. Now before you can get a bm for your digimon you need a few things:
A BM item- These unlock the bm/side mega slot of the evolution slot. You can get these from the cash shop or they are given out as event items every other month.
A lot of ds items/food- Bms eat 40 ds every 5 seconds.
A level 65 digimon- You can be any tamer level but you must have your digimon to level 65 before you can use your item to digivolve.
Lots of Accelerators- These are those little white circle things that you start getting in snow. You need 3 each time you digivolve to bm.
Now there is a difference between a BM and a Side Mega. Both require an item but aren't the same thing.
Burst Mode- Eats 40 ds per 5 seconds, uses 3 accelerators each time you digivolve and don't keep their level auras.
Side Mega- Eat 11 ds per 5 seconds, are generally not as strong as some other bms and keep their level aura.
To see your selection of bms and side megas going to the cash shop will tell you whats available and what digimon it affects. This place has most of the bm/side megas:
http://gdmo-guides.blogspot.com/2012/08/list-of-digimon-evolution-all-attribute.html
Some of the newer ones not included are:
Keramon's BM Armageddemon
DemiDevimon (Soulmon line) BM Chaospiedmon
Then there is something called a Jogress. These are fusions of two digimon creating some of the strongest digimon in the game. There are a few things you need to get these powerful digimon:
The two fusion digimon to at least level 41- When the jorgess is added generally joymax will post on their site what digimon you need and what to do to get the jorgess. These two digimon must have the mega slot unlocked and if they have bm/side mega cannot have that unlocked.
The Quests- These are the quest you need to do to unlock the jorgess slot for the digimon, each digimon will have their own set of quests (There are usually 4). Some of these quests might require you to have maze or b2, so if you know a jogress that you want is coming, then start leveling up. And no you can't have one of your high level friends go kill the stuff for you while you party with them. Joymax will also usually post a guide of what the quests entail so you know what to do.
The Jorgess Chip-You can buy these from the cash shop or supposedly certain digimon drop them. You have to have this chip applied or no jorgess. These are time limited chips, once they expire you have to buy more. They come in 30 days, 1 week or 1 day varieties.
Level 70 Tamer- You can do/get the quest even if your tamer isn't level 70 but you can't digivolve your digimon to jorgess form until you're level 70.
Lots of Chicken Combos and an aura- Tamer aura do not hold the jogress evolution. If you stand still than the aura will re-charge your tamer ds or if you don't move around much when you are killing things. In a place like the maze entrance where you're running all over the place, you will need chicken combos to help hold your evolution.
