They heat it, by different degrees depending on the polarization of molecules in the tissues and liquids. The molecules try to re-align after the radio-wave field and the movement dissipates as general heat. Think microwaves.. a consumer-grade microwave oven operates at the same radio wave spectrum as your home WiFi network (2.4 GHz) but much stronger.
The SAR, Specific Absorption Rate measures the amount of RF-energy deposited in the body in a well specified way (in W/kg) from a radio product. Cellphones have to be rated with this to be sold. I don't think the Hollywood Sign is rated with a SAR though... :)
Actually, the SAR for cellphones is measured using a dummy human head with similar dielectric properties as a real human head. This can pose problems when engineers try to bring these dummies as carry-on luggage through airport security screenings, a friend who works at a cellphone company mentioned ;)
There have been reports now and then on RF-waves doing more complicated, specific things with tissues like opening the blood-brain barrier etc. As far as I know none of these have been conclusively proved (in a human model) but this area of course features incredible pressure from health organizations, governments and huge industrial companies.
There usually is an "old story" from people in the military service where they heat water-bottles by hanging them in front of their mobile radar station.. I don't know if that is true in particular, but it can't be very good to hang out in front of strong omnidirectional radio-emitters even for no other reason than the tissue-heating :)