  Event Horizon Telescope (EHT) observations at 230 GHz have now imaged
polarized emission around the supermassive black hole in M87 on event-horizon
scales. This polarized synchrotron radiation probes the structure of magnetic
fields and the plasma properties near the black hole. Here we compare the
resolved polarization structure observed by the EHT, along with simultaneous
unresolved observations with the Atacama Large Millimeter/submillimeter Array,
to expectations from theoretical models. The low fractional linear polarization
in the resolved image suggests that the polarization is scrambled on scales
smaller than the EHT beam, which we attribute to Faraday rotation internal to
the emission region. We estimate the average density n_e of order 10^4-7 cm-3,
magnetic field strength B of order 1-30 G, and electron temperature Te of order
(1-12) x 10^10 K of the radiating plasma in a simple one-zone emission model.
We show that the net azimuthal linear polarization pattern may result from
organized, poloidal magnetic fields in the emission region. In a quantitative
comparison with a large library of simulated polarimetric images from general
relativistic magnetohydrodynamic (GRMHD) simulations, we identify a subset of
physical models that can explain critical features of the polarimetric EHT
observations while producing a relativistic jet of sufficient power. The
consistent GRMHD models are all of magnetically arrested accretion disks, where
near-horizon magnetic fields are dynamically important. We use the models to
infer a mass accretion rate onto the black hole in M87 of (3-20) x 10^-4 Msun
yr-1.
