An UART (universal asychronous receiver-transmitter) is commonly known as a serial port. While this mode of communication is considered slow and out-of-date, there are still many devices that can only communicate via asynchronous serial communication.
Note that although wired asychronous communication is pretty much a thing of the past, UARTs are still very useful because of Bluetooth. Bluetooth has a profile that allows devices to communicate via asynchronous protocols. Essentially, this means that if an embedded controller has an UART, it becomes very easy to communicate with it wireless via a dumb terminal emulator or a smart program that communiates via the serial port.
Applications: