Reactive programming is a programming paradigm based on the concept of an asynchronous data flow. A data flow is like a river: it can be observed, filtered, manipulated, or merged with a second flow to create a new flow for a new consumer.
A key concept of reactive programming is events. Events can be awaited, can trigger procedures, and can trigger other events. Events are the only proper way to map our real world to our software: we open a window if it's too hot inside. In the same way, we want the Total cell to update when we change some values in our spreadsheet (the propagation of the changes) or our robot to turn around the moment it reaches the wall (reaction to events).
Nowadays, one of the most common scenarios for reactive programming is UIs: we have mobile apps that have to react to network calls, user touch input, and system alerts. In this world, software has to be event-driven and reactive because real life is event-driven.