What are some of your favorite colloquial sounding names for mathematical objects, proofs, and so on? For example, manifolds are often described using an atlas and a neighborhood describes a small set surrounding a point.
I can't believe no one has yet mentioned the following. These were quite common, at least at one time (1970s).
abstract nonsense -- refers to (Eilenberg/MacLane) category theory
invariant under change of notation -- refers to differential geometry, especially when tensors are involved
proof by diagram chasing -- refers to a proof involving commutative diagrams, especially when the proof is essentially solving a path puzzle or hedge maze puzzle