Asymptotic behavior refers to the behavior of a function as its input approaches a certain limit, often infinity. It helps in understanding how functions grow or decay in relation to one another, particularly in fields like mathematics and computer science. This concept is crucial for analyzing the efficiency of algorithms, as it provides a way to compare their performance without needing exact values. In practical terms, asymptotic notation, such as Big O, Big Theta, and Big Omega, is used to describe these behaviors. For example, if an algorithm has a time complexity of O(n^2), it indicates that its running time grows quadratically as the input size, n, increases. This allows developers to predict how an algorithm will perform with larger datasets.