How does a NAND gate work using transistors?

[Young Learner]

http://www.dummies.com/how-to/content/electronics-projects-how-to-create-a-transistor-na.html

In the above link it is said that the output is logic ON if both the inputs are OFF.
What does that mean. Correct me if I am wrong.
As far as I have learned from the site was when the input is ON current flows from the supply to Vcc to the base and hence the transistor conducts and the currnet is sent to groung to the emitter. In case if the Input is ON there is no connection between the Vcc and the base and hence the current is obtained across the output.
Am I right?

 

[skeptic2]

Gates are voltage devices. A NAND gate with both inputs high will have an output at low voltage. In this example with both switches closed there is a high voltage at the switch side of resistors R2 and R3. This high voltage causes both transistors to conduct, causing a voltage drop across R1, resulting in a low voltage at the output.