  Pairing of fermions lies at the heart of superconductivity, the hierarchy of
nuclear binding energies and superfluidity of neutron stars. The Hubbard model
of attractively interacting fermions provides a paradigmatic setting for
fermion pairing, featuring a crossover between Bose-Einstein condensation (BEC)
of tightly bound pairs and Bardeen-Cooper-Schrieffer (BCS) superfluidity of
long-range Cooper pairs, and a "pseudo-gap" region where pairs form already
above the superfluid critical temperature. We here directly observe the
non-local nature of fermion pairing in a Hubbard lattice gas, employing spin-
and density-resolved imaging of $\sim$1000 fermionic ${}^{40}$K atoms under a
bilayer microscope. Complete fermion pairing is revealed by the vanishing of
global spin fluctuations with increasing attraction. In the strongly correlated
regime, the fermion pair size is found to be on the order of the average
interparticle spacing. We resolve polaronic correlations around individual
spins, resulting from the interplay of non-local pair fluctuations and
charge-density-wave order. Our techniques open the door toward in-situ
observation of fermionic superfluids in a Hubbard lattice gas.
