A human body exposed to space would not explode. It would freeze-dry, just like foods that are exposed to vacuum to preserve them.
At any temperature water and ice give forth water vapour until the [partial] pressure of that vapour reaches a critical pressure called the `saturated vapour pressure`, which depends on what material is involved and also depends on the temperature. A human body contains moisture, and will therefore give forth water vapour. But this will not accumulate to the point of satuartion: the molecules will gradually drift forth into the vastness of Space. So the body will gradually dry out.
As this moisture evaporates it will carry off heat: latent heat of evaporation. So the body will freeze as it dries. As its temperature drops the saturated vapour pressure of its internal moisture will also drop, and the drying process will slow down. So it may take quite some time for the body to freeze-dry itself.
As for a living person exposed to vacuum, the experimental results with chimpanzees and the occurences in an accident testing equipment as part of the Apollo Program both suggest that a person would pass out for lack of oxygen within about fifteen seconds, and would shortly die of anoxia. When he or she died his or her heart would ceased to maintain blood pressure, and only then, after death, would the freeze-drying of the body begin. There might, however, be some superficial injury, a combination of frostbite and chapping, which would affect the moist tissues of the eyes and respiratory tracts well before death.