The skip Mode is the only mode available during Friend Mode, the first part of the game. In this mode, time passes as fast (or as slow) as you can click through the events. This is helpful to zoom through the Friend Mode as it take approximately 50 game days to clear.
While in Lover Mode, Skip Mode offers simplified and accelerated play where you can quickly build up Boyfriend Power/Hearts and unlock features. Keep in mind though, that when in this Lover Mode, Skip Mode no longer saves the day of the week as it does in Friend Mode. Instead, every time you save & exit or switch between Real-Time Mode, the day of the week is reset to the current day on your DS clock. what this does is, if you schedule a date in Skip Mode, you have to finish the date before you end the session or switch modes. Otherwise it counts as not showing up for a date.