An atom has no overall electric charge, so we say it is neutral. This is because the number of protons in the nucleus is equal to the number of electrons around it.
Each proton has a charge of +1 and each electron has a charge of −1. When there are equal numbers of each, the positive and negative charges cancel out. Neutrons have no charge, so they do not affect this balance.
For example, an atom of carbon has 6 protons, so it also has 6 electrons. The total charge is +6 and −6, which adds up to 0. If an atom gains or loses electrons, the numbers are no longer equal and it becomes a charged ion.