What are those little short lines above and below the staff?

Leger lines (also written as ledger lines) are notation devices used to show notes that are too high or too low for the regular lines of a musical staff. A staff consists of five lines a four spaces, each of which correspond to a specific note. But notes that don't fall within those nine areas must go somewhere, so extra leger lines are drawn above or below the original staff to accommodate these notes. When learning to read music, young students often learn to recognize middle C early and quickly by its place on a leger line; it's represented by a leger line one place below E, which is the bottom line of a treble clef staff.

Leger lines are both extremely beneficiary and occasionally confusing, depending on the number of lines drawn. On the one hand, leger lines keep a piece of sheet music from jumping into different clefs for brief periods of time. Multiple clef changes can be difficult for musicians as each clef's staff represents notes differently. An F on a treble clef staff, for instance, is not an F on a bass clef staff. Leger lines help avoid this confusion by making extra space for high or low notes without having to incorporate constant and disorienting clef changes.
On the other hand, however, multiple leger lines can be too difficult to read. Notes located on three or four leger lines are usually engrained into a musician's sight-reading knowledge, but anything more than that can trip up the efficiency of a reading. It's difficult to smoothly read a piece of music while trying to count leger lines and figure out a very high or very low note. In these situations, a clef change is absolutely necessary. Still, it's the composer's choice whether or not to use leger lines here. If he or she is confident that those reading the music will be able to decipher it, leger lines may be used uniformly without a clef change, even if a clef change would be theoretically correct.