A chord extension is the addition of an extra interval to an existing chord. For example, C (C, E, G) → C7 (C, E, G and Bb) or Cm (C, Eb, G) Cm6 (C, Eb, G and A). There are also extension intervals which are placed into the next octave, such as the 9th. The 9th is the same note as the 2nd except it is usually found in a chord an octave higher. For example, C9 (C, E, G and D)
The following list outlines the commonly used extensions and their respective lower octaves. All these intervals are major intervals, unless otherwise indicated with sharps or flats, except the 7th which is always a minor seventh. The major seventh is specifically indicated as "maj7". The most common alternations of these extensions and their respective lower octave equivalents are also listed here.
b9 = minor 2nd + octave (only used on Dom7b9 chords)
#9 = augmented 2nd (minor 3rd) + octave (only used on Dom7#9 chords)
#11 = augmented 4th + octave (mostly used on Maj7(#11) or Dom7(#11) chords)
b13 = minor 6th (augmented 5th) + octave (mostly used on Dom7b13 chords)
Extensions are normally used to add some extra color to a chord to make it sound more interesting. They are more commonly played by chord instruments like guitar or keyboard, but can also be played by melody/solo instruments.
As a Bass player they have to be used more carefully and sparsely, because the bass instrument is the lowest instrument and should mainly establish the foundation of a chord which is the root note. Extension notes are good to use as passing notes.