What is the science behind using a persons body to extend a radio's strength?

The human body is actually a decent antenna. Your height determines what frequency is most resonant but generally we are broad band antennas meaning that we’ll receive signals over a wide range. Specifically we are really close to the FM range ~85–108mhz which makes us decent ½ wave antennas depending on posture. To get a better signal get a better antenna. Also, not going to give you cancer, Radio waves are non-ionizing radiation and the amounts we receive are trivial. One caveat is that yes some things can be harmful, you are actually supposed to keep cell phones an inch away from your head while talking. non-ionizing radiation obeys the inverse square law so distance is your friend and it’s surprising how little distance is needed to put you at a safe distance from even the most powerful transmitters. The miss-information about radio is epidemic.

@ARE_you_kidding_me

It appears that this is the definitive answer and nothing further can be said on the subject.

I always wondered about this too.
@talljasperman Thanks for asking.
@ARE_you_kidding_me Thanks for answering.

@ARE_you_kidding_me that is very informative, I did not know that, do you think that could work with portable TV?

Yes it can, worked better with old analog tv though.

@ARE_you_kidding_me got the ring with this one. I remember the old analog “rabbit-ears” TV antennas. Here is a funny story that rang true to me (additional emphasis added):
On occasion, getting a picture on the ol’ Admiral or the Philco meant talking, cajoling — or threatening — another household member into grabbing the base of the antenna while standing on their head and holding the rabbit ears pointed in the right direction with their left foot or some such. Even after all of these machinations, the outcome was never guaranteed.

Thanks for the comments guys, I do this sort of thing for a living and I’m a ham so this is 2nd nature. I could rant and rave for hours about radio.