Finding a name in the phone book
Reading a phone book cover to cover to find one name is painfully slow, but flipping to the middle and halving each time is fast. Big-O notation is how we describe that difference — how much slower a method gets as the data grows huge.
Growth, not stopwatch time
Big-O describes how an algorithm's work grows with input size n, ignoring constants. O(1) is constant, O(n) grows linearly, O(n²) quadratically.
Hash map lookup
Looking up a key in a hash map is on average O(1) — independent of how many items it holds.