A 'note' is what you hear when you push down and hold a single key on a piano. It is a sound with a given 'pitch' that is applied for a specific 'duration' in time.
When a single key is pressed upon a piano, what we hear is not just one frequency of sound vibration, but a composite of multiple sound vibrations occurring at different mathematically related frequencies. The elements of this composite of vibrations at differing frequencies are referred to as harmonics or partials. For instance, if we press the Middle C key on the piano, the individual frequencies of the composite's harmonics will start at 261.6 Hz as the fundamental frequency, 523 Hz would be the 2nd Harmonic, 785 Hz would be the 3rd Harmonic, 1046 Hz would be the 4th Harmonic, etc. The later harmonics are integer multiples of the fundamental frequency, 261.6 Hz ( ex: 2 x 261.6 = 523, 3 x 261.6 = 785, 4 x 261.6 = 1046 ).
Below is a logarithmic sonogram (created by my C++ software) for 3 seconds of a guitar solo on a mp3 recording. It shows how the harmonics appear for individual notes on a guitar, while playing a solo. You can even see how the guitarist is bending a note upward in frequency, just before the start of Note A.
You could read the linked Wikipedia article on Pitch Detection to get a more elaborate definition of a 'note' in musical terms.
A link for the C++ source code of my Pitch Detection software, which made the sonogram, is also below.