Protons are positively charged subatomic particles (a subatomic particle is a small part of an atom - protons, neutrons, and electrons). Electrons are negatively charged subatomic particles.
Just as is true with positively and negatively charged numbers in math, opposites charged subatomic particles cancel each other out. In order for this to be true, however, there needs to be equal numbers of positive protons and negative electrons.
If there are more protons than there are electrons, then the overall charge of the resulting atom will be positively charged. If there are more negatively charged electrons than there are positively charged protons, then the overall charge of the resulting atom will be negatively charged.
Charged particles are called ions. An anion is a negatively charged ion. A cation is a positively charged ion.