1. Part of the material of which the Earth was created was radioactive. Much of this radioactive material consisted of heavier atoms, forming dense solids, and formed the core of the Earth. Some of it however became part of the Earth's crust. Even though the Earth is about 4.5 billion years old, not all of this material has decayed. Uranium 238, the most abundant isotope of Uranium, for example has a half life of 4.5 billion years, so half of the radioactivity remain. This radioactivity is concentrated in certain areas e.g. Cornwall in the u.k. 2. The Earth is being bombarded with cosmic rays, which can create radioactive isotopes of atoms in the atmosphere. The best example is carbon - some of it becoming carbon 14. We breathe some in as CO2, and eat some, contained in food.
The radiation from these sources is called the 'background radiation'.