Style sweepers are important because they change the frequency at which a guitar will play. The two frequencies that a style sweeper changes between are slap and fingerstyle.
Fingerstyle is one of the most common ways of playing the guitar. It involves plucking the guitar strings with a fingertip or by using a pick. This allows different chords to be played on the guitar.
Slapping creates a more percussive sound, and is done by using the bony part of the thumb to strike the guitar strings, and allowing the strings to vibrate against the metal frets. This creates a buzzing sound, and gives the music more depth.