Undisturbed atoms are electrically neutral; the number of electrons is the
same as the number of protons. An atom that has electric charge is called an
ion. It might acquire this charge by losing electrons--in which case
the charge is positive--or by picking up some extra ones, making the charge
negative. The process of making an atom into an ion is called
ionization--hence the term "ionization energy."
Ions are formed in many chemical reactions.
Ionization can also be caused by radiation, such as high-energy photons or
charged particles. The key is to hit the atoms with enough energy to
shuffle electrons around.