The momentum threshold is a movement mechanic that stops the player from moving when their momentum is deemed negligible.
At the end of every tick, after applying slipperiness, the game considers the absolute value of the X and Z components; if one is smaller than 0.005, it is set to 0.
This same mechanic also affects the player's vertical movement, as the vertical speed at the peak of a jump would be equal to ~0.00302.
In 1.9+, The momentum threshold has been lowered to 0.003, which increases the jump height to ~1.252 (up from ~1.249).
Interestingly, the X and Z velocity components are treated independently in this process, which sometimes causes the player to move in a slightly slanted direction when only one of the components has reached threshold speed.
In other games, this threshold concept is usually applied to the velocity's norm instead, so that the player's direction is uniform.
Momentum threshold notably affects Tiers, Tapping and turn-based jumps.