Stacks are linear data structures where elements are inserted and removed from the same end, known as the top. Common stack operations include push to add an element, pop to remove the top element, and peek to view the top element without removing it. Stacks are often implemented using arrays or linked lists and have O(1) time complexity for operations. Some applications of stacks include reversing data, converting numbers between bases, expression conversions, and backtracking problems like N-Queens.