Normalization is a process of restructuring a relational database in order to bring its tables into one of the normal forms. There are several normal forms that define requirements to the structure of a table or, strictly speaking, a relation.
For example, a relation is in first normal form (1NF) only when each of its attributes contains a single value. To understand this concept, think about a table that contains a phone book where each record corresponds to a person. If a person has more than one telephone number, they all would be stored in a singe field, comma-separated, as follows:
SELECT person, phones FROM contacts; person | phones --------------+---------------------------------- John Smith | +1-254-4556-44587 George ...