The C7(b13) belongs to the category of altered dominant 7th chords (general: V7alt). These are dominant 7th chords with one ore more of the altered tensions b9, #9, b13 or #11 (which is a special case, since it rather comes along with the natural tensions 9 and 13. Please look up the description for a 7(#11) chord. The altered tensions b9, #9 and b13 mainly occur, when the V7 chord resolves from V to I, like from the C7 to Fmaj7 or Fm7. You may sometimes also stumble across the universal notation C7alt for a C altered chord, saying that the player can decide by himself which altered tensions he/she wants to use. An experienced guitar player will normally decide by himself anyway and for example just play a 7(b9) or 7(#9) chord where 7(b13) is written or the other way round.
C7(b13) theoretically consists of the tones C (1), E (3), G (5), Bb (7) and Ab (b13), but the 5th will practically always be abandoned for the b13, that on the guitar is located just one fret higher.
The b13 is located a minor 6th above a root, but it has to be written as b13 in the chord symbol and not as b6, because it is a chord extension. A 6th can only be written when there's no 7th. And a b6 is nearly inexistent in chord symbols, because those chords will mostly be reinterpreted as inversion of a related chord and then often be notated as slash chord.