The C7(13) or just C13 is a dominant 7th chord (V7) with an additional major 6th. Because the 6th is extending the 7th chord rather than replacing the 7th, it is written as 13 in the chord symbol.
A C7(13) respectively C13 has the notes C (1), E (3), G (5), Bb (7) and A (13). The 5th can be omitted. In practise you’ll often take it and move it up 2 frets (a whole-step) to play the 13.
In most cases a C13 chord can be played instead of a plain C7. Especially if the C7 chord is resolving from V to I (like C7 to Fmaj7 or Fm7), is often preferred or even obligatory to play a C7(b13) with the altered tension b13 instead of the natura tension 13, following the same rules as a C7(9) respectively C9 chord, where in some cases a b9 or #9 should be preferred or obligatory.
In jazz V7 chord are rarely played without either natural or altered and sometimes even mixed up tensions.