Even though two instruments can play in the exact same pitch they sound different. This is interesting since a pitch (a note) is simply a frequency. The note A on the third string second fret of the guitar should the frequency of around 440 Hz depending on tuning. This note has the same frequency independently of what instrument plays it and should, in principle, sound exactly the same with all instruments. The reason this is not so is that instruments do not produce a single frequency.
While an instrument may be playing an A (440 Hz), it is producing other frequencies as well, some of which are higher (overtones) and some of which are lower (undertones). Overtones and undertones are not as pronounced as the fundamental frequency that is being played, but they do change how an instrument sounds.
Timbre is the quality of a sound defined by the overtones and undertones contained in that sound.
Different instruments produce sounds with inherently different qualities even if they play in the same pitch. Those qualities of the sound are the sounds timbre.