An element's identity is determined by the number of protons it has. The basic structure of an atom is that there are protons and neutrons in the nucleus, and electrons that are orbiting at set distances from the nucleus. Electrons are negatively charged, protons have a positive charge, and neutrons are neutral/have no charge. The atomic number of the element means the number of protons it has. For example, all oxygen atoms have eight protons; all nickel atoms have 28 protons.
When the atom overall is uncharged, the number of electrons equals the number of protons. Atoms can exist in a charged state. These are known as ions. Positively charged ions have lost electrons; negatively charged ions have gained electrons.
Isotopes of atoms exist. In isotopes, the proton number is constant but the number of neutrons varies as does the resulting atomic mass (which is the number of protons plus the number of neutrons). Carbon exists as both carbon-12 and carbon-14, depending on the number of neutrons it has, but all carbon has 6 protons.