A normal linked list only allows navigation in one direction. That means from node n, you can only reach node n+1. A doubly-linked list allows navigation in either direction. From node n, you can reach both node n-1 and node n+1.
The real difference between a linked list and an array list has to do with how they are implemented "behind the scenes." You'll use the two almost as if they are the same but the way they are implemented is very different. An array list uses as a backbone an array. (Big surprise, huh?) A linked list, on the other hand, uses a number of "nodes" which reference the nodes before and after themselves in the list. Each implementation allows you to store multiple items in a list format and each one has some benefits and hindrances.
I suggest checking out
this article from a past edition of the JavaRanch Journal.
As this seems to be a question about
Java, in general, rather than specifically for the
SCJP certification, I'm moving this
thread to Java in General (Intermediate).