Based on your description, I too thought like Tim that you were referring to glissando but listening to the recording, I think these are simply arpeggios on the left hand while the right hand is simply repeating two notes.
The right hand shouldn't present much challenge here, so you just need to practice your arpeggios.
One way to practice them is to play by position: i.e. you play as many of the notes as you can at once and then you move your hand to play the next group of notes. This will help you memorize where your fingers should go. You will also need to strengthen your fingers as well, and work on the most difficult transition where the fingers move over your thumb by, for example, repeating that transition multiple times when you play the arpeggio.
There you have your crash course on playing arpeggios assuming this is indeed what you wanted to learn about :-)