Stack is a fundamental data structure in computer science that operates on a Last-In-First-Out (LIFO) principle. This means that the last element added to the stack will be the first one to be removed.

It is analogous to a stack of plates: you can only take the top plate off the stack, and when you add a plate, you place it on the top.

Stacks are vital in computer science and programming for several reasons:

1. Function Call Management: Stacks are used to keep track of function calls and local variables.

2. Expression Evaluation and Parsing: Stacks are essential in parsing expressions (such as converting infix expressions to postfix notation) and in evaluating postfix expressions.

3. Backtracking Algorithms: Algorithms that involve backtracking, such as solving mazes, puzzles (like Sudoku), or navigating decision trees, often use stacks to keep track of the path or decisions taken.

4. Undo Mechanisms: Many software applications, such as text editors and graphic design tools, use stacks to implement undo functionality.

5. Memory Management: Stacks are used for memory management, particularly in allocating and deallocating memory dynamically.

6. Syntax Checking: Stacks help in checking the syntax of expressions, particularly in verifying balanced parentheses, brackets, and braces in code.

7. Algorithm Implementation: Many algorithms, especially those involving recursion, can be implemented using stacks to avoid stack overflow and manage the algorithm’s state explicitly.

Overall, stacks provide a simple, efficient, and elegant way to manage data and control flow in various computing processes, making them a foundational tool in computer science.