This technique is known as Wobbling. That's because of Wobbles, a professional player who was an Ice Climbers main.
Wobbling begins with a grab by Popo. Following this, the Ice Climbers player must use one of many methods to desynch the Ice Climbers, and have Popo pummel while Nana forward tilts or down tilts. If done correctly, Popo and Nana will hit the enemy repeatedly in an alternating rhythm while the enemy cannot escape. This technique can inflict significant damage, and can lead to a KO if Nana performs a forward smash after sufficient damage has been inflicted.
In addition to standard Wobbling, a variation called Blizzobbling can also be performed, where Nana instead uses Blizzard to attack opponents instead of using a tilt. Like Wobbling, it is also inescapable.
Wobbling works by the existence of a mechanics exploit in Melee. When an opponent is grabbed, they cannot mash out of the grab if the character grabbing them is performing an attack. This is the basis behind how pummeling works; opponents cannot mash out when a pummel connects, but pummels are not fast enough to stop them from escaping in-between them. However, Popo and Nana are treated as the same character when attacking. Thus, players can exploit desynching to force them to attack in an alternating manner that does not allow enough time for any character to escape from the grab; the delay between the pummel and the tilt is miniscule if not nonexistent, and is humanly impossible to escape from.
You perform a grab as Popo and desync Nana by using some variation of a tilt (there are many ways to desync the Ice Climbers). You can then hit the enemy in such a way where they cannot tilt out of your grab.
A great video on the technique can be found here: SSBM Ice Climbers Wobble
You can learn more about Wobbling here: Wiki - Wobbling