Local coordinates describe a position or direction relative to a particular object or parent, rather than the whole scene.
The object brings its own directions
Think of a label attached to a rotating sculpture. The label can stay a short distance above the sculpture even while both move around the room. Its local position describes that relationship. A point inside a mesh is measured in the mesh’s own frame; an object’s local transform is usually measured relative to its parent. These are related uses of the same idea.
Local axes and local position are not identical
A move tool set to local orientation follows the selected object’s rotated axes. A numeric position field, however, may still describe its origin relative to its parent. Editor interfaces differ, so do not assume that switching the gizmo also changes how every number is displayed. After a quarter turn, moving along local X can point in a different room direction from world X.
When it helps an artist
Use a local relationship when several elements should travel together: petals around a flower, lettering beside an object, or parts of an animated figure. When preparing a GLB for Painta, inspecting these relationships in the source file can explain why a part moves unexpectedly after its parent rotates. The animation compares fixed world directions with directions that turn with an object.