Antiferromagnetic order and fluctuations in the heavy-fermion superconductor URu2Si2 have been studied by magnetic neutron scattering. Below T(N) = 17.5 K, URu2Si2 is a type-I antiferromagnet with an anomalously small ordered moment of (0.04 +/- 0.01)mu-B polarized along the tetragonal c axis. Dispersive resonant excitations exist in the ordered state with a zone-center gap of 0.43 THz. The excitations are polarized along the ordered moment and have a large dipolar matrix element, which suggests that they are coupled transitions between singlet crystal-field-like states. For energy transfer above 3 THz, peaks have not been identified in the magnetic excitation spectra, but instead a continuous spectrum of scattering peaked around the ordering wave vector indicates the presence of overdamped antiferromagnetically correlated spin fluctuations. Upon heating above T(N), the resonant excitations abruptly become heavily damped but the magnetic scattering at higher energies does not change at T(N). Instead, the disappearance of the antiferromagnetic modulation of the higher-energy scattering coincides with the maximum in the resistivity of URu2Si2.