Linked lists are data structures that allow for flexible storage of data in memory compared to arrays. They consist of nodes that contain data and a pointer to the next node. This allows nodes to be added or removed without affecting other nodes and their performance is better than arrays for insertions and deletions. Common types of linked lists include singly linked lists, doubly linked lists, and circular linked lists. Key operations on singly linked lists include inserting and deleting nodes from the front of the list using pointers and dynamically allocating memory for new nodes.