In analytics we like to track every interaction of a user with the system. Whenever a user interacts with our system we record an event. This event usually contains an id which can uniquely identify the user. This id can be a cookie, an IP address or a Vendor ID from an iOS App. Active Users is the number of unique users who interacted with the system. Active users are calculated over a time-period, e.g. Monthly Active Users (MAU), Weekly Active Users (WAU) or Daily Active Users (DAU). So when you want to calculate MAU, you would gather all the events in the last month and count the number of unique ids. This means that Active Users is the cardinality of the set of all the ids from these events.