I noticed the term BUS in the startup procedure of a 737. What do BUS on, off and transfer mean and what is their significance?
A bus is a strong connection that distributes current. It's not limited to the conductive part, it is usually understood as including the switches and relays that manage its connection to the rest of the wiring.
(Keep in mind that with AC, when two different sources are used to feed the same component, frequency and phase need to be adjusted and must coincide, else energy would be lost, and voltage increased / decreased, possibly to a dangerous level.)
The transfer buses in that case have a logic detecting multiple current sources, e.g. battery and ground supply, and selecting which one to use to feed the bus. The crew has some authority on this process, using switches:
There is one transfer bus on each side of the aircraft. They feed other buses, like galley and main buses, with energy, typically from the engine generators.
They are connected by the tie bus (between BTB1 and 2 on the image, it's name doesn't appear), for redundancy purposes.
Boeing 737 NG, modified (source)
Before the two engines are running (and their generator supplies current), the tie bus allows the ground power, or the APU, or a single engine to feed the whole aircraft.
Transfer buses can be disconnected from the tie bus for normal use, each engine generator providing energy to different smaller buses, creating a redundancy.
If one source fails, the other can feed the whole aircraft by connecting the tie bus. Another connection can be used on the DC part (cross-bus tie relay). This mode is useful and required when performing an approach with the autopilot (e.g. ILS cat III).
Conversely if one transfer bus creates a security problem, it can be switched off.