  (Abridged) We present deep, sub-horizontal branch, multi-colour photometry of
the Andromeda II dwarf spheroidal (And II dSph) taken with Subaru Suprime-Cam.
We identify a red clump population in this galaxy, the first time this feature
has been detected in a M31 dSph, which are normally characterized as having no
significant intermediate age populations. We construct radial profiles for the
various stellar populations and show that the horizontal branch has a nearly
constant density spatial distribution out to large radius, whereas the reddest
red giant branch stars are centrally concentrated in an exponential profile. We
argue that these populations trace two distinct structural components in And II
and show that this assumption provides a good match to the overall radial
profile of this galaxy. The extended component dominates the stellar
populations at large radius, whereas the exponential component dominates the
inner few arcminutes. We show that the two components have very different
stellar populations; the exponential component has an average age of $\sim 7 -
10$ Gyrs old, is relatively metal-rich ([Fe/H] $\sim -1$) but with a
significant tail to low metallicities, and possesses a red clump. The extended
component, on the other hand, is ancient ($\sim 13$ Gyrs), metal-poor ([Fe/H]
$\sim -1.5$) with a narrower dispersion $\sigma_{\rm [Fe/H]} \simeq 0.28$, and
has a well developed blue horizontal branch. The extended component contains
approximately three-quarters of the light of And II and its unusual density
profile is unique in Local Group dwarf galaxies. This suggests that its
formation and/or evolution may have been quite different to other dwarf
galaxies.
