What happens in the nucleus of an atom when an alpha particle is emitted

An alpha particle or helium nucleus consists of 2 protons and 2 neutrons.

So the atomic mass (number of protons and neutrons) of the element decreases by 4 and the atomic number (number of protons) goes down by 2.

The loosing of the 2 protons causes the element to change.

Gamma radiation will also be emitted although this can be some time after.