The slight difference in ground potential between your finger and the circuit ground means that your finger will produce a very small voltage on the base of the transistor. This is enough to turn the transistor on, which pulls the I/O pin on the MCU low.
The site recommends a normal NPN transistor, but these circuits normally work better/more reliably with a darlington or sziklai transistor pair, as they give a much higher gain, which will better amplify the tiny voltage applied to the base (though keep in mind transistors are transconductance devices)