Your Skills are the special powers you have access to during battle. There are two primary types, with sub types in those categories.
Your super attacks are the staples of the Dragon Ball universe. Supers are moves such as the Kamehameha, Galik Gun and Masenko. During battle, you can use a super attack at any time, so long as you have enough Ki to do so.
Super attacks come in dozens of shapes and sizes, such as energy beams, explosions and even melee focused attacks. They also have various charge times, with the Kamehameha taking several seconds to charge, where as the Double Sunday is instantaneous.
The several sub types of Super Attacks are:
Your ultimate attacks are the most powerful tools available to you. Much like Super Attacks, your ultimate attacks can come in different shapes and sizes as well as having energy based ones or melee ones (Strike Super, Ki Blast Super, etc...).
Ultimate attacks take much more Ki to launch, often requiring 300 or more. They also trigger small scenes, and generally can't be cancelled once they have begun.
The Evasive Skills are what you expect, special skills to get you out of bad situations. Sometimes they are knock back explosions, or teleportation abilities. If timed right, you can dodge any attack.
For a complete list of the different Skills available in the game, check out the Skill List page.