Trains with more than one engine at the front often seem to have at
least one engine facing backward, so that it apparently runs in
reverse.  What purpose is served by this?

To pull it when the train needs to "turn around" and head in the other
direction, silly!

Actually, it's a bit more complex - well, not really.

The other locomotive pushes the train.  You usally see this on long
freight trains, and you sometimes even see a locomotive in the middle
of the train.  This is done to reduce tendency to stall, especially on
a grade, allows the train to stop quicker, and also reduces the forces
on the couplings, meaning longer lasting freight cars.

Check out this site for more info:

http://www.wordiq.com/definition/Locomotive

And if you are really interested in trains, check this site out:

exotic.railfan.net

This newsgroup post may be of interest:

"Any modern diesel locomotive pulls just as well in 'reverse' as it
does forward... Many times a railroad will assemble a loco consist
back to back, or if more than two, the ones at the ends will face
opposite directions. This is so the consist can be run back in the
opposite direction without turning, since most facilities don't have
turnarounds of any kind."

http://groups.google.com/groups?selm=3e18f88b.1556763116%40news.iac.net&output=gplain