The function of a session cookie in web applications is to store user-specific information during a browsing session. When a user visits a website, the session cookie is created to retain essential data about their activity, such as login status or items in a shopping cart. This cookie is temporary and expires once the user closes their browser. By using session cookies, websites can maintain state and offer a personalized user experience, minimizing the need for users to re-enter data or log in repeatedly.