Big O notation is a mathematical framework for describing the asymptotic behavior of algorithms as input size grows toward infinity. Born from computational complexity theory, it abstracts away hardware specifics and constant factors to reveal the fundamental scalability of code—whether an algorithm remains practical at scale or collapses under growing data. While Big O represents the upper bound (worst-case), companion notations like Big Omega and Big Theta capture lower bounds and tight bounds respectively. The key insight: an $O(n)$ algorithm doubles runtime when input doubles, but an $O(n^2)$ algorithm quadruples it—this multiplicative difference dominates performance at scale, making complexity analysis the single most powerful lens for predicting real-world algorithmic behavior before a single line executes.