Data structures are a way to organize data in a computer so it can be used efficiently. Common data structures include arrays, stacks, queues, linked lists, trees, and graphs. Arrays store elements in a linear order, stacks follow last-in first-out access with push and pop, queues are first-in first-out using enqueue and dequeue, and linked lists, trees and graphs have nodes connected by links or edges. These data structures enable efficient operations like inserting, deleting and searching for data.