The core of the atom contains a nucleus. That nucleus is made up of protons and neutrons.
Protons are made up two up quarks and a down quark. Up quarks have a charge of +2/3 and down quarks have a charge of -1/3.
+2/3 + 2/3 -1/3 = +4/3 - 1/3 = +3/3 = +1. This means that protons have a positive charge.
Neutrons are made up of two down quarks and an up quark.
-1/3 - 1/3 + 2/3 = -2/3 + 2/3 = 0. This means that neutrons have no charge, or a neutral charge.