An array is a data structure that stores a collection of values in a single entity. In SQL, an array can be used to store multiple values in a single column of a table.

There are various operations that can be performed on arrays in SQL, such as:

1. Declaring an array: An array can be declared in SQL using the ARRAY keyword. The syntax for declaring an array is: ARRAY[element1, element2, ...].
2. Accessing elements in an array: The elements of an array can be accessed using the [] operator. For example, to access the second element of an array named my_array, you can use my_array[2].
3. Adding elements to an array: Elements can be added to an array using the || operator. For example, to add an element 'new_element' to an array named my_array, you can use my_array || 'new_element'.
4. Removing elements from an array: Elements can be removed from an array using the - operator. For example, to remove an element 'old_element' from an array named my_array, you can use my_array - 'old_element'.
5. Sorting an array: The ORDER BY clause can be used to sort the elements of an array. The syntax for sorting an array is: SELECT * FROM table_name ORDER BY column_name ASC|DESC.
6. Searching for an element in an array: The IN operator can be used to search for an element in an array. The syntax for searching for an element in an array is: SELECT * FROM table_name WHERE column_name IN (element1, element2, ...).

Here is an example of how you can use arrays in SQL:

CREATE TABLE users (
id INT PRIMARY KEY,
name VARCHAR(255),
hobbies ARRAY[VARCHAR(255)]
);

INSERT INTO users (id, name, hobbies)
VALUES (1, 'John', ARRAY['soccer', 'swimming']),
(2, 'Jane', ARRAY['reading', 'painting']);

SELECT * FROM users WHERE hobbies IN ('soccer', 'swimming');

This will return the following result:

id | name | hobbies
---|-------|------------------
1 | John | {soccer, swimming}