The willingness attributed to the notes is really about the expectations we have as listeners. For reasons that are some combination of acoustics, our auditory system, and cultural norms, we perceive some sequences of notes as creating tension, and others as resolving that tension.
When you hear a musical line that resolves, it sounds finished. When you hear one that doesn't resolve, it sounds like there's another note that needs to be played to finish it.
Different people emphasize different ones of these factors in their theory of how this works, but one thing we can mostly agree on is that different arrangements of notes played together or in sequence convey different moods or emotions in a way that is fairly predictable, at least within a given cultural context. So composers can intentionally write happy or sad or suspenseful songs or whatever using music theory.
The musical modes can be thought of as a single pattern of note intervals across an octave, but starting on different notes in the sequence. The standard way to lay out the modes is to start with a scale that is called the Ionian mode, the diatonic scale, or the Major scale.
These names all refer to the same pattern of intervals. Counting semitones, this pattern is 2-2-1-2-2-2-1.
(The "2" means two keys on a piano, or two frets on a guitar, for example.)
If you play that pattern, you will hear the familiar major scale in the key that is named by the first note you play. If you start on C, it's C Major.
The other modes are the same pattern, but starting on different notes. If we continue to use the notes of the C Major scale, leaving the pattern where it is, then starting on D instead of C gives us the Dorian mode (in the key of D). Its pattern is 2-1-2-2-2-1-2 -- in other words, exactly the same set of intervals as the Ionian mode, but shifted by one.
If you keep moving the starting note up by one, you get each of the other modes: Phrygian, Lydian, Mixolydian, Aeolian, and Locrian.
Each mode has its own mood or emotional character. The Aeolian mode, for example, is the same sequence of intervals as the Natural Minor scale, and tends to sound melancholy or wistful.
A simple trick for hearing what a mode sounds like is to sit down at a piano, find the first note of the mode you're interested in, and play the first note against each of the other notes in sequence up and down the scale. It's easiest to do if you start with the Ionian mode in C, because it's simply all the white keys on the piano, starting with C and going up to the right. So, to hear what the Ionian sounds like, play C, then C and the white note immediately to the right of it at the same time, then the next white note, then the next, all the way up to the next C (and,optionally, back down again).
If you repeat this exercise, but start on D instead of C, you'll hear that the scale has a different character. Keep going, and you get a nice sense of what each mode sounds like. Dorian's cheerful; Aeolian's melancholy; Phrygian's a little exotic; Locrian is just weird and never seems to resolve.