Ticks
Ticks are the standard unit of time in Minecraft, with one tick being equal to 50 milliseconds.
Relevant Minecraft Wiki Articles:
Tickrate
The physics engine runs at 20 ticks per second, meaning the game's physics are updated every 50ms.
This includes the player’s position and speed, the environment, and entities.
In-game actions are performed at the end of each tick, regardless of the time or order in which they were called.
Due to the game working this way, inputs may take up to 50ms of delay, with the average delay being 25ms.
Turn Tick
Mouse Movement is not inherently tied to tickrate, but rather the framerate (the graphics engine is independant from the physics engine).
But the game still keeps a copy of the Player's rotation in memory for calculations, and updates it every tick (just like keyboard inputs).
The term turn tick refers to the manifestation of tickrate delay in mouse movement.
Suppose you turn 45° smoothly over the course of 50ms. There is no way to predict what rotation will be kept in memory, as the copy could have been made anytime between 0ms and 50ms. Even if you repeat the same turning, at the same speed, the rotation stored might be completely different.
This is especially troublesome for jumps that require precise mouse movement, as they can be impossible to do consistently due to turn ticks.