Timbre is a word used to describe the particular quality of the sound of a single note of an instrument. It is what makes a oboe sound different from a flute, even when playing the same note.
Texture is a similar word that is sometimes used to describe this kind of thing, but texture is often used to describe a more general concept resulting from the mixture of sounds and instruments being played.
The Timbre of an instrument is it’s distinctive sound which is usually simplified to refer to the harmonics of the fundamental note being played. This is a simplification, but it is a useful one.
Almost every musical instrument makes its notes by hitting a real physical object (piano, percussion), vibrating air in a tube (woodwind, brass) or vibrating a string (Violin etc., Guitar). Each of these, and other ways to make notes, results in vibrations at the frequency of the note being played. There are also vibrations at a selection of higher frequencies that are a result of the physical properties of the instrument itself.
The higher frequency oscillations are usually multiples of the fundamental frequency, but can be slightly different. The position and strength these higher harmonics explains the differences between the different Timbres that we hear for different instruments.
Timbre is an app that wraps this spectrum around a circle so that one octave is one revolution around the circle. This makes any harmonics at a C, in any octave, appear at the same place.
A clarinet note has harmonics that look a little like this:
Read here for more details.