Why is my wiring hooked up like this
The video is wired differently, because the power (feed) goes to the switch first in that situation.  In your situation, the power (feed) is at the light. 

In your box, the feed comes in and the white grounded (neutral) conductor is connected to the grounded (neutral) conductor of the light, and presumably a feed to another branch of the circuit. The black ungrounded (hot) conductor is connected to a feed to the switch (white wire), and again presumably a feed to another branch.  The other conductor from the switch (black wire), is attached to the ungrounded (hot) conductor of the light. 

If you follow the circuit, power comes in to the box and goes to the switch. When the switch is closed, power comes back to the light. Once through the light, the circuit is completed back to the "neutral" wire.

To make this installation safe. Use twist-on wire connectors to make; and insulate, all connections.