Figure 1 shows an example of two measures that might appear in a slow ballad. The second measure contains a rhythmic pattern that is often misinterpreted. In this case, there is an eighth note on beat 3 tied to the preceding half note. Ask any classical musician what the duration of this figure is and he will probably answer, "two and a half beats." While that is correct for classical music, it is incorrect in a jazz context! In jazz, this note sounds for exactly two beats: the tied eighth note is an indication to stop the note on beat three.
As a verbal direction, we say "off on three" and may notate the reminder in our chart (in pencil!) with "-3" as shown in figure 2. Some published charts may print this performance direction as a courtesy.
Similar situations may also appear in straight-ahead swing charts. Also, the "off on ..." notation (e.g. -4) may appear on notes that are not tied to an eighth, typically at the end of a song, an example of which is shown in figure 3.
These conventions are not arbitrary. A composor or arranger uses these notations when he wants an immediate and definite stop to the sound on a specific beat. For example, it may be that the band is crescendo-ing to a climax with a dramatic cut to a delicate solo line - to be effective, the climax can not "hold over" else it "step on" the solo. The collective agreement on where, exactly, to stop a note makes for a "tight" performance. In the case of figure 3, it is often the case, especially in older big band music, that the final beat will be a bass/drum "bump".