Why doesn't aluminum foil burn my fingers when I touch it after it has
been in a hot oven?

Hello.

Here is a good explanation of this phenomenon courtesy of Argonne
National Laboratory's "Ask a Scientist":

"...How come when I put a pizza in the oven, the aluminum foil does 
not get hot?
...Author: mooney
...  It (aluminum foil) DOES get hot.  In fact it gets hot much more 
quickly than the nearby pizza.  It also cools off much more quickly,
which is
why we tend to think of it as not getting hot.  Here is the deal:  At
any
given temperature, aluminum holds much less energy than an equivalent
mass of
pizza (or an equivalent mass of human flesh--and now we are getting to
the
point).  When you touch the aluminum foil, your hand and the foil
share the
thermal energy in the foil. Your hand says "big deal!  It takes MUCH
more energy to raise my temperature because I am made mainly of water"
 (and water  is phenomenal in its ability to hold energy without
increasing temperature much).  However, it is also true that the
aluminum foil is much less massive than your hand, and so part of the
answer is that there is just not much foil there.  And its also true
that the air cools the foil more quickly than the  pizza since the
foil has more surface area in addition to holding less energy per
degree of temperature"
source: "Ask a Scientist," hosted by anl.gov:
http://newton.dep.anl.gov/newton/askasci/1993/physics/PHY62.HTM

search terms: foil, mass, heat, cools

I hope this helps.

I do agree with the answer by juggler-ga.  Here is a more
scientific version:
There are two physical properties of the aluminium are involved,
"specific heat capacity" and "thermal conductivity".
specific heat capacity accounts for the amount of heat that the
aluminium foil could store.
thermal conductivity accounts for how fast the material could
conduct heat(just like how fast an electrical wire could conduct
electricity).  Actually there are three ways in which heat conduction
occurs: conduction, convection, radiation. conduction involves no movement
of the molecules but requires physical contact. Convection is due to movement
of molecules(the way hot water moves up and down), radiation does not
involve direct contact or even air molecules(the way sun emits light rays).
Incase of the aluminium foil conduction and convection are the main processes
involved(conduction from the heated layer in contact with the pizza, to the
surface, and convection of the heat from the surface through air molecules
touching the surface of the foil).
What happens when you touch a aluminium foil, it transfers heat to your skin/
flesh. But due to the low specific heat capacity of the foil, the foil loses
the heat energy fast barely raising the temperature of the skin in contact.
This applies to the surfaces sufficiently away from the pizza.  If you do touch
the foil that is perfectly in contact with the pizza immediately after taking
out, you could get severe burn(because of the high thermal conductivity the
aluminium will conduct the heat stored on the pizza directly and continuosly
to your skin- to simplify, you could imagine as if the aluminium does not
exist and that you are touching the surface of the pizza crust).  But due to
high thermal conductivity, the foil transfers heat to the surrounding fast
and cools down very soon, which leaves the pizza surface in contact with the
aluminium cooler and due to the poor thermal conductivity of pizza, more heat
from the core of the pizza will not arrive at the surface of pizza keeping the
aluminium foil cooler.

Regards
ldavinci-ga