They're just clarifying the onset and direction of the nystagmus so you can differentiate it from central vertigo. So it will take a little while for the nystagmus to start and it will only be in the horizontal direction, c.f. central vertigo where it starts right away and can be in any direction (so if you see vertical nystagmus you know it has to be central, etc).
Unless you're asking for the mechanism of why you specifically get that pattern of nystagmus in peripheral vertigo, in which case I can't help.