Simply put, four-momentum transfer is the special relativistic
spacetime analog of classical (three-) momentum transfer. In
classical physics, two bodies can interact and exchange momentum in
three spacial dimensions. In particle physics, strictly spatial
momentum vectors do not suffice. Instead we use four-momentum, a
Lorentz vector.
Four-momentum transfer is often referred to as Q^2 is particle
physics literature. An interaction that transfer a large amount of
four-momentum is a high Q^2 interaction.