They run an embedded Linux operating system on the coprocessor, which in principle allows you to run programs on it, as if it were an ordinary albeit weird independent computer (see here
https://software.intel.com/en-us/articles/building-a-native-...). That is you can ssh on the device, etc. There are also various tools sold by Intel all with three digit price tags (I believe), that allow you to program with parallel directives for example and which translate that to something that runs on a xeon phi. You can also use OpenCL, in which case it presents itself as one of several OpenCL devices you can use.