Understanding how Schematic works
So there is a big difference between a bread board and a schematic.  The breadboard has internal connections that don't span the columns.


As for what this would look like if it were a schematic, it is fairly simple.


You are using the wired inputs to control the transistor as a switch.  This allows for greater current to flow through to the led to give you light from your power supply.

Remember that a picture of a breadboard is not a schematic, it is how the highway system looks when implemented.  The schematic is the roadmap, and although the roads layout can be different (breadboard, pcb, etc), you still will get to the destination.