The digi-burst is the new ability of LV6 digimon. These 3 all have "Digi-Burst 2", meaning trash 2 card to trigger 1 effect.
For green [ST4-13] Herculeskabuterimon: by trashing 2 cards from this digimon's digivolution source, it can trigger the effect: Rest 1 of opponent's digimon. This effect is very valuable, it is equal to playing a Flower Cannon (2 costs) to rest 1 opponent's digimon.
For black [ST5-13] Blitzgreymon: by trashing 2 cards from this digimon's digivolution source, 1 of your digimon gets +4000DP until end of your opponent's next turn. This effect can be useful for the black non-reboot digimon that is resting after attacking in this turn. Adding 4000DP can protect it from getting destroy in opponent next turn.
For violet [ST6-13] Cresgarurumon: by trashing 2 cards from this digimon's digivolution source, you can play a LV3 purple digimon from trash for free. This is totally useful for Purple since the color super-ability is to revive digimon from trash. There is no mentioning in the card that you can or cannot trigger "when played" effect of that LV3 digimon, so i guess it can use "when played" effect.