In this video, we discuss the implementation of an efficient queue data structure using a linked list approach. We start by analyzing the inefficiencies of a naive implementation where adding elements to the end of the queue requires traversing through all existing elements, resulting in a linear cost. To overcome this, we introduce a more complex implementation that uses two instance variables: `head` and `last`, which point to the first and last elements of the linked list respectively. This allows us to add new elements to the end of the queue with constant time complexity, making the enqueue operation very cheap. We also discuss how to implement the dequeue operation efficiently using this approach.