To put it simply, the scale length of an instrument is the distance between the string nut and the bridge on the guitar, which will determine the placement of frets for proper intonation up and down the fretboard.
The scale length of an instrument will affect the spacing of the frets, and ultimately, the feel of the instrument and the sounds that it can produce.
Technically speaking, a shorter scale will result in lower tension to bring the strings to pitch, whereas a longer scale will result in greater tension to bring the strings to the same pitch.
These differences in tension will affect the locations of the harmonics and overtones of each string, which can drastically influence the tone of the instrument as it is heard through the pickups and amplifier. Harmonics and overtones describe the resonant frequencies that can accent the “note” of an instrument to give it a distinct and musical sound.
Guitars with shorter scale lengths will historically have more dense overtones and harmonics, whereas guitars with longer scale lengths will historically have more articulated highs and lows, with clear notes.
Some PRS guitars will indicate the scale length in the name of the model -- such as with the McCarty 594 (which has a 24.594” scale length), or the Singlecut 245 (which has a 24.5” scale length). The scale length of each model is listed in the SPECIFICATIONS section on the product page.