The tail profile can have a large impact as to how that ski reacts; mostly it changes how the ski exits a turn.
Twin Tiptail shapes are where the tail of the ski is turned up as much as the shovel is. A twin tip allows you to ski and land backwards. Twin tips are not only reserved for freestyle skis, there are many all mountain options that are twins. A twin tip will help your ski exit a turn very quickly, especially when you are in bumps or moguls.
Flared tail shapes are moderately turned up and tapered slightly. This is the most common and most versatile tail shape that still has grip at the end of your turn for strong carves, but will release the ski with little effort.
Flat tail skis are most common in aggressive carving skis, or race skis. Flat tails give you grip and power until you decide to exit the turn, and then require a little extra effort to exit, and they ski best at high speeds.