A Musical Note, in its most fundamental definition, is a defined frequency of audible sound. It’s the most basic building block of musical theory. In modern musical theory, a note is defined universally no matter what genre of music you are in or musical instrument you are playing.
There are 12 basic notes in an octave. European culture has assigned abstract values to these notes to make it easier to express ideas using them. The note annotations range from A to G, with ‘sharp’ or ‘flat’ to fill the 5 gaps. The distribution of these notes, and their sharps and flats, are based on the layout of the traditional piano, with the letters falling on the white keys, and the flats and sharps falling on the black keys.
The black keys, or the sharps and flats, have two different names assigned to them that you can refer them as. The key between the C and D can either be called C Sharp (C#), a half-step above C, or D Flat (Db), a half-step below D.
Notes are usually assigned lengths based on a beat, or tempo. The definition starts with a whole-note, then half-notes, which are half the length of whole notes. Then quarter notes, which are a quarter length of whole notes, and so on.
In the graphic above, the top note is known as the whole note. The two notes that are below the whole note are known as the half note, while the four notes below the half notes are known as the quarter note. As you can see, each succession of notes are half the length the previous succession and therefore it takes twice as many notes to fill in the same time as before.
The overall definitions of the beat of a note is assigned by a time-signature. A beat is a point in a steady rhythm that is used to define measures.
In the first time signature above, the bottom number ‘4’ indicates that the value of a ‘quarter note’ is the beat. In the second time signature, the bottom number ‘8’ indicates that the ‘half note’ is assigned the beat. In the last time signature, it is the ‘eighth note’ that is assigned the beat.
When a particular note is assigned the beat, all other notes are relative to it. For instance, if the bottom number is ‘4’, the quarter note is assigned the beat. This means that the half note is now 2 beats, while the whole note is 4. An eighth note is 1/2 a beat, while the sixteenth note is 1/4 a beat.
I will stop here. Let me know if this is an adequate job of explaining these concepts in the comments below. For those who are thinking this is a bit basic, I figured I would cover the absolute basics before getting into the more advanced stuff.