'order' has many meanings in mathematics, and I'm not sure of the best metaphor that is actually called an order there, but when people talk colloquially about 'second order effects' etc. IME they mean something like a vertex v2 (doing something) in response to a change to v1, where there exists a vertex vj and edges (v1, vj) & (vj, v2) - and implicitly no edge (v1, v2). Higher 'orders' similarly extending the chain.

Or think chess - 'first order thinking' would make a move that merely escapes mate, or puts you in a position where another move immediately could be a great one; 'second order thinking' considers what the opponent will do from there (probably disallow the great move or threaten it back); etc.