Avoid Note

Literally "avoid notes," it is a term used by Americans to indicate certain notes of a scale that do not belong to the extensions of the relative chord or that are considered so dissonant as to be "avoided." Naturally, the term avoid is excessive; these are notes that are primarily used as passing notes. For example: C major chord, C major key, obviously C major scale; the avoid note in this case would be the IV degree (F):

the root, the 3rd, the 5th and eventually the 7th or 6th are chord tones, the 9th is a harmonic tension; the only one left out is the 4th (perfect, in this case).

Personally, I do not love these extreme schematizations of USA-made teaching; in the end, it's enough to try singing or playing an F held over a C major chord to understand that it's better to move elsewhere promptly ;-)

The discussion is different for modal music; here I am in sharp disagreement with the classification of avoid notes like the one we find on Wikipedia: I am of the opinion that in this context there are no notes more dissonant than others; in fact, the major 6th of the Dorian mode is considered an avoid note, when this is precisely its characteristic note!

I respond with a joke: Avoid Notes are "the notes that one must avoid not playing".

For the rest, I agree with Dr. Jellyfish. Of course they allow you to... stay within the chord, but if you want to go beyond the chord, the chromatic scale is composed of 12 notes, many of which are out-of-scale, and at the right moment and in the right place, they embellish the composition or improvisation.