Can someone explain this project to me? Can you explain the schematic so I understand how it works?
I was going to say "read the description on the page you linked to", but the description there is wrong. (don't believe everything you see on the Internet!)

An LDR will have a high resistance in the dark, and low in light.  

If light hits the LDR, it will have a low resistance, pulling Q1's base up.  Q1 will turn on, pulling its collector, and Q2's base low, so Q2 will be off, and the relay will be released, turning the light off.

If the LDR is in the dark, it will have high resistance, allowing Q1 to turn off, so Q1's collector and Q2's base go high, pulling Q2's collector low and turning the relay on.