In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, to submanifolds in manifolds, and suitable subsets of algebraic varieties.
For affine and projective algebraic varieties, the codimension equals the height of the defining ideal.
This statement is more perspicuous than the translation in terms of dimensions, because the RHS is just the sum of the codimensions.
In other language, which is basic for any kind of intersection theory, we are taking the union of a certain number of constraints.
This quip is not vacuous: the study of embeddings in codimension 2 is knot theory, and difficult, while the study of embeddings in codimension 3 or more is amenable to the tools of high-dimensional geometric topology, and hence considerably easier.