The often-seen schematic showing that alpha radiation is not as penetrating as gamma rays doesn’t tell the whole story. Alpha particles are highly dangerous, due mainly to their high charge (they are +2, due to their 2 protons) and mass. Alpha particles do not pass through the skin. However, if they somehow do find their way inside the body, they are devastating.
Polonium 210 is a radioactive isotope of polonium, which is element 84, on the right side of the periodic table. (See if you can find it.) Polonium 210 is highly unstable, and its nucleus self-destructs by giving off an alpha particle. For this reason it is called an alpha emitter. If swallowed, inhaled, or injected into the body, polonium 210 will emit alpha particles, which do not have to penetrate the skin. For this reason, it is 250,000 times more poisonous than cyanide.
The radioactivity associated with (for example) a nuclear explosion would be mostly caused by radioactive dust, unavoidably inhaled into the lungs. In 2006, an ex-KGB agent named Alexander Litvinenko died of polonium 210 poisoning, likely assassinated by a fellow spy.
The more you know.