Sacudían comes from the verb sacudir, which means "to shake" or "to shake off". It's a very physical and evocative word that you don't often find in romantic songs.
In "La Distancia", Manuel Medrano sings, "...como tus manos sacudían todos esos problemas de mí" (how your hands would shake all those problems off of me). He uses this powerful image to describe how a lover's touch could literally make all his worries disappear, creating a beautiful and memorable picture of comfort and relief.
This song by Colombian artist Manuel Medrano is a beautiful, bittersweet look back at a past relationship. He starts by remembering all the little physical details he'd almost forgotten, like how good it felt to touch her skin and how her hands could make him forget "lo cruel que era el mundo" [how cruel the world was]. It's clear they aren't together anymore, as he remembers her kisses "aunque ya no estés aquí" [even though you're not here anymore].
But this isn't just a sad song about a breakup. It's full of hope. He begs her, "Ojalá que nunca se te olvide" [I hope you never forget] about their plan to meet again. He believes that the time and space between them, "la distancia" [the distance], will actually heal the hurt they caused each other. He's holding on to the idea that one day they'll look at each other again and know that their connection was too strong to ever really end.