Can anyone help explain this schematic?
You appear to provide the schematic of the ST-Link-V2 side of a larger PCB. There are lots of different discovery/"nucleo"/eval boards from/with ST that include an ST-Link adapter and a target µC. The signals T_SWCLK/T_SWDIO/T_SWO and STLK_TX/STLK_RX go from the ST-Link controller to (the level shifter towards) the target controller, which sadly is not depicted in the question post. The former three signals mentioned above are the SWV connection (two signals SWD plus one for optional SWO tracing), while the latter two signals connect a full-duplex UART link to the target, which is provided by the ST-Link adapter and may be used to connect to the application target µC and help debug it or implement a bootloader.

Please note that the STM32F103CBT6 is the ST-Link controller. It is meant to be connected to a PC through the USB connector in the upper right corner.

As a next step you should inspect the other pages of that schematic (there must be some, because this page alone would be useless nonsense). Additionally, STM provides nice User Manuals for its Nucleo/Discovery boards, which include lots of detail information on different features - a good starting point to learn working with ST's development boards. Good luck.