The left-pointing arrow in the action bar is actually an "Up" button. It works a bit differently than the back button -- instead of going back to the screen you visited last, it goes to the screen that's one level up the hierarchy.
Google's Developer Guide gives a detailed look:
The Up button is used to navigate within an app based on the hierarchical
relationships between screens. For instance, if screen A displays a
list of items, and selecting an item leads to screen B (which presents
that item in more detail), then screen B should offer an Up button
that returns to screen A.
If a screen is the topmost one in an app (that is, the app's home), it
should not present an Up button.
The system Back button is used to navigate, in reverse chronological
order, through the history of screens the user has recently worked
with. It is generally based on the temporal relationships between
screens, rather than the app's hierarchy.
When the previously viewed screen is also the hierarchical parent of
the current screen, pressing the Back button has the same result as
pressing an Up button—this is a common occurrence. However, unlike the
Up button, which ensures the user remains within your app, the Back
button can return the user to the Home screen, or even to a different
The Back button also supports a few behaviors not directly tied to
Dismisses floating windows (dialogs, popups)
Dismisses contextual action bars, and removes the highlight from the selected items
Hides the onscreen keyboard (IME)
EDIT: Take a look at the Google I/O video explaining the reasoning behind having both.