[charles Tauber]

The short answer is that most (Western culture) music has an identifiable key Center that is given by a key signature. Music often changes keys within a single piece. In some cases the key signature is changed mid piece while in other cases the key change is temporary and achieved through accidentals (sharps, flats and naturals).

A D# is found in the key of E, suggesting a temporary key change to E. E major is the “dominant” (fifth) of A, one of the most common of chord/harmonic progressions. The D# is found in a B major chord, the “dominant” of E, which is the dominant of A: B major is the fifth of the fifth of A. As others have said, that’s likely what the study you are working on is doing: it is a very common harmonic progression.