A pipe is a data stream, typically data being read from a file or from a network socket. A broken pipe occurs when this pipe is suddenly closed from the other end. For a flie, this could be if the file is mounted on a disc or a remote network which has become disconnected. For a network socket, it could be if the network gets unplugged or the process on the other end crashes.
In Java, there is no BrokenPipeException specifically. This type of error will be found wrapped in a different exception, such as a SocketException or IOException.