There are two types of charges which we see in nature: They are positive charges and negative charges.
Like charges refer to positive-positive/negative-negative charges whereas unlike charges refer to positive-negative/negative-positive charges.
Repulsion refers to the force which makes two charges move away from each other while attraction refers to the force which makes two charges come in contact with each other.
A positive charge contains an excess number of protons in it whereas a negative charge contains a less number of protons in it. When a positive charge is brought closer to a negative charge, excess number protons from the positive charge get transferred to the negative charge, so that the number of protons in both the charges is balanced. This virtual transfer of protons from a positive charge to a negative charge causes an attractive force between them.
Now, when a positive charge is brought closer to another positive charge, once the virtual transfer of protons occurs, there is an excess number of protons in both the charges, which tend to repel them away from each other. The same happens when two negative charges are brought closer. But here, it is the excess number of electrons, which causes repulsion among the two negative charges.
Therefore, like charges repel and unlike charges attract.