This touch is based on monostable mode of NE555 timer chip. Simply follow the schematic shown on the video and touching the wire connected to pin 2 of NE555 will turn on the LED connected to pin 3 of NE555.
The LED stays on for some time when you touch the wire and the duration depends upon the values of resistor and capacitor shown on the schematic.
This is one of the easiest projects for electronics beginners. You can also build a dark sensor using the monostable mode of NE555.