There are three types of radiation commonly emitted by
radioactive elements when they decay.  Before it was
known what they were they were labeled
alpha, beta and gamma.
We now know alpha are Helium nucleuses (big, heavy, slow)
beta are electrons (light, fast)
and  gamma are electromagnetic (like X rays but more so)

Alpha will not penetrate skin, so an alpha emitter OUTSIDE
the body is harmless.  But if you get it inside, then it can damage
or kill tissue BIG TIME.

Gamma will penetrate, but what makes it able to penetrate also
means it is unlikely to do anything.   You need massive amounts
of gamma to do tissue damage.

Beta is in between.  More penetrant and less damaging than alpha,
less penetrant and more damaging that gamma.

In the radioactive iodine treatment, a radioactive form of iodine
is ingested.  Since the thyroid concentrates iodine, it normally
ends up there.  If a gamma emitting RAI is used, you "light up"
the thyroid for diagnostics, but at the low amounts used, no
appreciable tissue damage is done.  For RAI thyroid destruction
a different RAI is used, either a beta or an alpha emitter.  SO
a small amount will do lots of damage to the thyroid gland.

The RAI decays fast.  But the killed thyroid tissue remains for
a bit until the body resorbs it.  (How fast does a "back and blue"
fade away on you?  Same process will resorb the killed thyroid
tissue, takes a bit longer though.)

If you have Grave's eye disease, note that RAI has higher
incidence of eye complications than surgical removal of
the gland.  However, surgery has many complications
also - vocal cord and/or parathyroid damage, scarring.
And for many people control by thyroid suppressant drugs
works well.  

Now if this is not technical enough, I can go into linear
energy transfer and momentum vs. energy issues.  Tissue
damage mechanisms by free radical formation (only that
is more Ted's area than mine) and ionizing radiation.  But
I expect that is not what you are interested in.  If you
are, just ask.  But I tried to present the major issues without
so much technical gobbledegook.
--
Kevin G. Rhoads, Ph.D. (Linearity is a convenient fiction.)
T_Rhoads@NO_SPAM.MSN.com
krhoads@NO_SPAM.cmpnetmail.com