I heard my band teacher talking about "scale degrees" and do not understand what he means.
Supposing you know that music notes named cdefg or doremifasol are ascending like a scale (meaning a ladder or a stair) so a degrees is a single step of this scale.
But the band leader might also have meant the triads of thirds that are built on each degree: e.g. domiso or ceg. (If you skip always one note you get thirds and fifths like 135. You can play the tones 1-3-5 from any degree of an instrument. On the piano the degrees are the keys in the scale of C major the white keys.
Study the pattern of triads (chords) on a piano keyboard and you will get the idea of scales and degrees. If we play the row of white keys we get the C major scale. Starting with C = I ,D =II,E=III ...
As we've seen the scale degree can mean the single tone of each step, but also the chord on each step of this ladder.
There are 7 different notes in (most) scales. (The 8th is a repeat of the first.)
C, D, E, F, G, A, B. The seven notes of C major scale. Or the 1st, 2nd etc. degrees of the scale. That is what 'degree' means.