The amount of radiation given off by a radioactive material (the radioactivity of a source, whether it is alpha or beta particles, gamma rays, x-rays, or neutrons) is measured in Bq (or in Ci).
The radiation absorbed by a person (how much your cells absorb) is given in Gy.
For the biological risk of exposure to radiation (the harm done to your body), the measure used is Sv. And as the different particles (α,β, γ, X-rays) ionise differently, it is usually expressed as a “dose equivalent” in Sieverts (Sv).
Moreover, as the Sievert is quite a large unit, you are more likely to come across millisieverts (mSv) or microsieverts (μSv).
A good way to think of it is to imagine you are under heavy rain. The amount of rain falling is in Becquerels, the amount of rain hitting you is in Grays, and how wet you are is measured in Sieverts.
2.4 mSv/year (0.27 μSv/h avg)
Human exposure to natural background radiation, global average[a]
24 mSv/year (2.7 μSv/h avg)
Natural background radiation at airline cruise altitude
average dose to people living within 16 km of the Three Mile Island nuclear power plant in 1979.
5 to 10 μSv
one set of dental X-rays
0.4 to 0.6 mSv
banana equivalent dose, an illustrative unit of radiation dose representing the measure of radiation from a typical banana
US legal limit on effective dose from a single airport security screening