1.
dimension (mathematical/physical)
A measurable extent in physics and mathematics, such as length, width, height, or time. Used in scientific and technical contexts.
2.
level, plane (figurative)
A level or plane of thinking, discussion, or existence. Used figuratively to indicate that something is on a completely different level from something else.
Etymology
次 (order, sequence) + 元 (origin, element). In mathematical usage, refers to independent directions of measurement.
Usage
The expression 次元が違う is extremely common in everyday Japanese, meaning "on a completely different level" or "in a league of its own." In otaku culture, 二次元 (2D) refers to anime/manga characters, while 三次元 (3D) refers to real people.