I think you mean double pointer as in "pointer to a pointer" which is very efficient for inserting at the end of a singly linked list or a tree structure. The idea is that you don't need a special case or a "trailing pointer" to follow your traversal pointer once you find the end (a NULL pointer). Since you can just dereference your pointer to a pointer (it points to the last node's next pointer!) to insert. Something like this:
T **p = &list_start;
while (*p) {
p = &(*p)->next;
}
*p = new T;
instead of something like this:
T *p = list_start;
if (p == NULL) {
list_start = new T;
} else {
while (p->next) {
p = p->next;
}
p->next = new T;
}
NOTE: It is also useful for making efficient removal code for a singly linked list. At any point doing *p = (*p)->next will remove the node you are "looking at" (of course you still need to clean up the node's storage).