An array is an ordered sequence of items (‘elements’) (see: http://en.wikipedia.org/wiki/Array_data_type)
Each element can be of any data type.
You may also have another array or a hash as an element of an array, in this example we have an array of arrays:
You can create an array in a formula using the ARRAY function. E.g.
ARRAY(1, 2, 3)
A hash is an associative array (http://en.wikipedia.org/wiki/Associative_array), or in other words a mapping of keys to values.
Names to ages
A hash is designed to allow you to get the value associated with a key very quickly.
You can do this in a formula:
HASH_GET($hash, "Steph") // result is 10
Hashes are also used in several places to pass in named arguments to functions, for example in DB_LOOKUP.
To create a hash in a formula use the HASH function. E.g.
HASH("name", "Alfred", "age", 24)