BGScript is a Basic-style programming language used to implement user applications in the Bluetooth® module.
It abstracts the complexity of the Bluetooth® protocol, scheduling, memory management, etc. so that user applications can be easily implemented. It is an event-driven programming language, so code execution is triggered by events (eg system startup, Bluetooth® connection, I/O interrupts, etc.).
The sample code is also substantial, so you can design it with reference to them.

Please also refer to the SiliconLabs community site for the differences between BGAPI and BGLIB.