Double Jump Cancel Countering (DJCC) is a technique unique to Yoshi. Yoshi's second jump has knockback protection, 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.
In action, simply double-jump at an opponent, within their attacking range. He will likely attack you, you will absorb the hit (taking all applicable damage), and be able to immediately counterattack, or float away in the direction you were previously headed. Any aerial or B-move can be done immediately after impact, but the most common are Yoshi's faster aerial attacks (such as neutral aerial), and the neutral B swallow attack. In Super Smash Bros. for the n64, this technique is one form of the many parries of smash 64. It is overall easier to parry in smash 64 due to the long invincibility range of Yoshi's up b.