Its the npn transistor. The finger in the picture serves as the high ohmic resistor through which the base of npn is getting a small positive current.
When the npn gets a small positive current into its base, larger collector current flows from positive to the negative through emitter and into the LED.
Placement if the current limiting resistor for LED is not important. It can be before or after the LED.
However the circuit works well if the following is done.
1. LED and its current limiting resistor should be on collector at the positive side if the battery.
2. The base must be connected with a resistor such as 4.7K ohm to prevent possible huge base current which will blow the base-emmiter junction.