The double jump cancel counter, abbreviated DJCC, is a technique unique to Yoshi in all five installments of the Super Smash Bros. series. Yoshi's midair jump has armor and will continue its momentum after the appropriate freeze-frames are applied against all but the strongest attacks. The DJCC utilizes this protection to allow Yoshi to jump into an opponent, take a hit, and proceed to follow up with a counterattack almost immediately.
The technique starts with double-jumping at an opponent within their attacking range. They will likely attack the player, and the player will absorb the hit (taking all applicable damage), and be able to immediately counterattack or float away in the direction they were previously headed. Any aerial or special move can be done immediately after impact, but the most common are Yoshi's faster aerial attacks (such as neutral aerial) or his Egg Lay.
In Smash 64 and Melee, this technique is one form of the many parries of the game. It is overall easier to parry in Smash 64 and Melee due to the long invincibility range of Yoshi's double jump compared to Brawl and the fourth game. High level CPUs in Smash 64 are also surprisingly proficient at using this technique, likely due to their very quick reflexes.
The technique is also somewhat limited in Brawl and Smash 4 because Yoshi continues to rise after he throws the attack, making it harder to aim and follow up.