Minecraft wiki entry for execute, associated text: Updates the command's execution position, aligning to its current block position (an integer). Only applies along specified axes.
This is akin to flooring the coordinates – i.e. rounding them downwards.
Syntax
align <axes> -> execute
Arguments
<axes>: swizzle
Any non-repeating combination of the characters 'x', 'y', and 'z'. Axes can be declared in any order, but they cannot duplicate. (For example, x, xz, zyx, or yz.)
Result
Execution position in the given axes are floored, changing by less than 1 block.
Unparseable if the argument is not specified correctly.
Example
Given (-1.8, 2.3, 5.9), /execute align xz changes the position to (-2, 2, 5).
Given (2.4, -1.1, 3.8), /execute align yxz run spawnpoint @p ~ ~ ~ sets the player's spawnpoint to (2, -2, 3).