What Makes Them Special?
Special Attacks are moves that require a specific controller motion or a combination of buttons to perform. For example, Scorpion's Spear requires a Back, Back + Front Punch sequence to perform, Raiden's Teleport requires a Down, Up input to perform, and Sub-Zero's Ice Ball requires a Down, Forward + Front Kick to perform.
Special Attacks generally are more powerful than Normal Attacks and cause your character to perform attacks that have much farther range, provide unique movement, fire projectiles, and on and on. Also, every character has a few Normal Attacks that can be buffered into a Special Move, allowing for combos. For example, Liu Kang and perform a Front Punch into Front Punch Kombo Attack and cancel the second Front Punch into the Flying Dragon Kick for a 3-hit combo.
What's Your Specialty?
Special Attacks are, generally, what separates the characters from each other. They are what makes Kitana feel much different than Jax and Sindel feel much different than Cyrax and so on and so forth. Special Attacks will form the basis of your gameplay, and most of your strategies will revolve around these moves.