Electrostatic repulsion refers to two particles of the same charge that drive away each other. For example, a positively charged particle will repel another positively charged particle.
An atom has subatomic particles called electrons, neutrons and protons. Electrons are negatively charged, while protons are positively charged. Neutrons have no charges. Both neutrons and protons are located in an atom's nucleus. Many elements have atoms with more than one proton. Considering how protons repel each other, protons should not be in the atom's nucleus together. But, due to the exchange of mesons, there is a strong nuclear force which holds the protons together. Another reason is because of neutrons, which act as a barrier for the repelling force.