Scale Degrees

A scale degree is just a numbered position: 1 through 7, counting up from the tonic. Every mode has seven of them, but the numbers alone don't say what note actually sits at each position - for that, every mode gets measured against the same reference: Ionian, the major scale. Ionian's own seven notes are the plain, unaltered degrees - 1, 2, 3, 4, 5, 6, 7, no sharps or flats attached - which is what makes it the yardstick everything else is described against, rather than one more mode with equal claim to the naming.

Lydian is Ionian with the 4th degree raised a semitone: sharp 4.

Aeolian (natural minor) is Ionian with the 3rd, 6th, and 7th degrees each lowered a semitone.

This is the same tonic held fixed while the degrees move - a parallel comparison. See Comparisons for more mode pairs described this way, one degree at a time. Chords, not just notes, get numbered from the tonic too - see Roman Numeral Notation.