SPL provides a set of standard datastructures. They are grouped here by their underlying implementation which usually defines their general field of application.
A Doubly Linked List (DLL) is a list of nodes linked in both directions to each others. Iterator's operations, access to both ends, addition or removal of nodes have a cost of O(1) when the underlying structure is a DLL. It hence provides a decent implementation for stacks and queues.
Heaps are tree-like structures that follow the heap-property: each node is greater than or equal to its children, when compared using the implemented compare method which is global to the heap.
Arrays are structures that store the data in a continuous way, accessible via indexes. Don't confuse them with PHP arrays: PHP arrays are in fact implemented as ordered hashtables.
A map is a datastructure holding key-value pairs. PHP arrays can be seen as maps from integers/strings to values. SPL provides a map from objects to data. This map can also be used as an object set.