  (Abridged) We report results from a comprehensive study of the nearby M dwarf
Proxima Centauri with the XMM-Newton satellite. We find strongly variable
coronal X-ray emission, with flares ranging over a factor of 100 in peak flux.
The low-level emission is found to be continuously variable. Several weak
flares are characteristically preceded by an optical burst, compatible with
predictions from standard solar flare models. We propose that the U band bursts
are proxies for the elusive stellar non-thermal hard X-ray bursts suggested
from solar observations. A very large X-ray flare was observed in its entirety,
with a peak luminosity of 3.9E28 erg/s [0.15-10 keV] and a total X-ray energy
of 1.5E32 erg. This flare has allowed to measure significant density variations
from X-ray spectroscopy of the OVII He-like triplet; we find peak densities
reaching up to 4E11 cm^-3 for plasma of about 1-5 MK. Abundance ratios show
little variability in time, with a tendency of elements with a high first
ionization potential to be overabundant relative to solar photospheric values.
We do not find significant effects due to opacity during the flare, indicating
that large opacity increases are not the rule even in extreme flares. We model
the large flare in terms of an analytic 2-Ribbon flare model and find that the
flaring loop system should have large characteristic sizes (~1R*). These
results are supported by full hydrodynamic simulations. Comparing the large
flare to flares of similar size occurring much more frequently on more active
stars, we propose that the X-ray properties of active stars are a consequence
of superimposed flares such as the example analyzed in this paper. Such a model
also explains why, during episodes of low-level emission, more active stars
show hotter plasma than less active stars.
