  In this paper we present observations, simulations, and analysis
demonstrating the direct connection between the location of foreground emission
on the sky and its location in cosmological power spectra from interferometric
redshifted 21 cm experiments. We begin with a heuristic formalism for
understanding the mapping of sky coordinates into the cylindrically averaged
power spectra measurements used by 21 cm experiments, with a focus on the
effects of the instrument beam response and the associated sidelobes. We then
demonstrate this mapping by analyzing power spectra with both simulated and
observed data from the Murchison Widefield Array. We find that removing a
foreground model which includes sources in both the main field-of-view and the
first sidelobes reduces the contamination in high k_parallel modes by several
percent relative to a model which only includes sources in the main
field-of-view, with the completeness of the foreground model setting the
principal limitation on the amount of power removed. While small, a
percent-level amount of foreground power is in itself more than enough to
prevent recovery of any EoR signal from these modes. This result demonstrates
that foreground subtraction for redshifted 21 cm experiments is truly a
wide-field problem, and algorithms and simulations must extend beyond the main
instrument field-of-view to potentially recover the full 21 cm power spectrum.
