  The DArk Matter Particle Explorer (DAMPE), a high energy cosmic ray and
$\gamma$-ray detector in space, has recently reported the new measurement of
the total electron plus positron flux between 25 GeV and 4.6 TeV. A spectral
softening at $\sim0.9$ TeV and a tentative peak at $\sim1.4$ TeV have been
reported. We study the physical implications of the DAMPE data in this work.
The presence of the spectral break significantly tightens the constraints on
the model parameters to explain the electron/positron excesses. The spectral
softening can either be explained by the maximum acceleration limits of
electrons by astrophysical sources, or a breakdown of the common assumption of
continuous distribution of electron sources at TeV energies in space and time.
The tentive peak at $\sim1.4$ TeV implies local sources of electrons/positrons
with quasi-monochromatic injection spectrum. We find that the cold,
ultra-relativistic $e^+e^-$ winds from pulsars may give rise to such a
structure. The pulsar is requird to be middle-aged, relatively slowly-rotated,
mildly magnetized, and isolated in a density cavity. The annihilation of DM
particles ($m_{\chi}\sim1.5$ TeV) into $e^+e^-$ pairs in a nearby clump or an
over-density region may also explain the data. In the DM scenario, the inferred
clump mass (or density enhancement) is about $10^7-10^8$ M$_\odot$ (or $17-35$
times of the canonical local density) assuming a thermal production cross
section, which is relatively extreme compared with the expectation from
numerical simulations. A moderate enhancement of the annihilation cross section
via, e.g., the Sommerfeld mechanism or non-thermal production, is thus needed.
