A tetromino's orientation, with regards to Tetris refers to the different ways that tetromino can exist after rotations.
Normally all the tetrominoes have a total of nineteen orientations, but probably to make things more symmetric, newer games (first BPS, then Tetris Guideline starting with 2002 Tetris Worlds) add six orientations: two for S, Z, and I. Adding 3 more orientations for O can become 2017/2018 standard.
Orientations can be described either by the way they point (especially for T, which at least one reviewer has compared to a finger gesture (link --ages 30+, contains sex references, nsfw)) or by the way the longest flat side faces. They may also be described as numbers: 0 = spawn orientation, 1 = rotate 90 after spawn, 2 = two rotations after spawn, 3 = rotate -90 after spawn.