Neutron scattering from single crystals has been used to determine the magnetic structure and magnon dynamics of FePS3, an S=2 Ising-like quasi-two-dimensional antiferromagnet with a honeycomb lattice. The magnetic structure has been confirmed to have a magnetic propagation vector of kM=0112 and the moments are collinear with the normal to the ab planes. The magnon data could be modeled using a Heisenberg Hamiltonian with a single-ion anisotropy. Magnetic interactions up to the third in-plane nearest neighbor needed to be included for a suitable fit. The best fit parameters for the in-plane exchange interactions were J1=1.46, J2=-0.04, and J3=-0.96 meV. The single-ion anisotropy is large, Δ=2.66 meV, explaining the Ising-like behavior of the magnetism in the compound. The interlayer exchange is very small, J′=-0.0073 meV, proving that FePS3 is a very good approximation to a two-dimensional magnet.