Aka: Atari ASCII, Atari Charset
ATASCII is the character set used by the Atari series of 8-bit computers (see: Wikipedia). It consists of only 128 characters and is therefor much smaller than other well known charsets like form the Commodore C64 or Amstrad CPC which do have 256 characters.
Here the complete charset including control codes:
ATASCII Art is the composition of art works out of ATASCII characters.
In contrast to ATASCII Art following art forms are much better known and wider spread: ANSI Art, ASCII Art, PETSCII Art,...
ANSI and ASCII are very popular on the PC.
The Amiga also has his kind of ASCII art.
The C64 is well know for it's PETSCII which is used as art form but also in games, demos, etc.
There are only a few releases, that use ATASCII like the demo 16384.
You can use native tools on the Atari. A good one is: ARTur.
Alternatively, if you prefer to work on modern PCs, you can use Mad Studio or Playscii.