The list is endless but they are essentially a set of tunes that have become an established repertoire for Jazz musicians the world over. There are several lists you can google for that perport to be definitive but, in reality, the list is changing all of the time as some tunes are added and others fall into disuse.
The real hardcore Jazzers tend to know these tunes by the hundred and are able to transpose them into any key at the drop of a (hi) hat. There are a range of fake books/real books (pretty much the same thing) that are legal and illegal that contain many but never all of the 'must know' standards. I do not consider myself to be a hard core Jazzer and only know about three.
There are the show tunes standards but there are also 'Jazz' standards (often Parker, Miles Davis, John Coltrane heads etc but again the list is massive e.g.All Blues is not a show tune but it is known by almost everyone, tunes like Bolivia, Airegin, Tenor Madness, Monk tunes etc).
This is a massive subject and one that can tie you up for life. A lot of Jazzers believe that, in order to make any headway into the music, you need to 'deal with' the standards but there are others who never bothered with them and find their own way - no roght or wrong, just different.