When you start looking at Jazz lead sheets, you might notice a Chord with the Alt modification. This is an altered chord.
You can play anything and call it an altered chord. You can sit on the Piano if you really want to. OK, maybe not quite…
The Dominant 7th chord allows a lot of leeway. Pretty much any note works over it to some degree. The clash of the tritone between the third and the seventh just opens up the possibilities.Thus, pianists started introducing all sorts of voicings to the chord. The obvious first note to add was the b9.
Why is this obvious? Well, an Natural 9 actually sounds pretty tame. The b9, OTOH, is the tritone of the root. This is the blues note of the relative dorian blues, and the 7th that turns the natural minor to the harmonic minor.
Ok, that is a lot of words. An example helps. G7. Dom7th of the C major scale. A flat over a G7. The enharmonic G# is the 7th of the A Harmonic minor scale, and the the blues note of the D dorian blues. It is the note that turns the C major scale into the C Bebop scale. The G7 includes the notes of the B dim triad. The Ab makes it a B half diminished chord. Thus, the two get used somewhat interchangably.
Once that got established in the Jazz tradition, the race was on to see that else could be altered. Some threw a #9 in there, some a #5, some a #4 tritone off the root . The root, fifth and even the thirds notes of the chord were often dropped in the voicings
These chords are often played deep in the heart of a sequence. The most obvious is a ii V7 I. There the V7 is often played as a tritone substitution, so ii bII I .
Again, in the key of C:
Dmin Db7 C.
The Db shares the two notes of the tritone with the G7: the B and the F. So, is the chord played a Db or is it a G7 + Db and G#? Only the pianist know for sure, and he already forgot.
Its just easier to write it as altered.