It doesn't, especially. The phone is a bridge between the continuous glucose monitor and the pump. Pairing two devices to a common piece of technology is easier to troubleshoot and less error-prone than trying to make the two devices talk to each other directly, and allows some of the work to be offloaded to a general purpose computer rather than having to build all of that into the devices themselves. These are things that have to work, so reducing the number of things they have to do is a safety feature. The phone can also share data from the monitor whenever it's online, versus the old situation where you'd have to bring your monitor in and hope your care team remembers to download the results.
Some pumps do pair directly to the monitors, but that often locks you into a specific configuration of monitor and pump and often costs more.