Local

It operates the local axis for each object.

local

[Local] command can change the shape based on a parent-child relationship and can move the vertices accurately along the local axis on the same plane.

For example, if you use regular [rotate] command only, it becomes difficult to move an object along the axis after rotation because the rotation angle is reset once it is rotated. When you rotated the local axis, you can move an object along the local axis with [L] button in Edit option for [Move] command.