Tables are used where a field can hold multiple values. There are simple tables, such as the Other Names: (Person Details) field in the Parties module:

Person Details - a simple table

This table can hold multiple values (a person could have many Other Names). There is only one column in this table, and each row holds a single value.

There are also more complex tables, such as Associated With on the Associations tab of the Parties module:

Associated With - a complex table

In this case there are multiple columns in the table and each column holds different details, thus each row in the Associated With table can hold multiple values.