Your body is an antenna and when you touch the base of this transistor some amount of electricity is coupled into that input of the transistor. This transistor is setup as an "emitter follower" which means that it will attempt to keep the voltage at the emitter (Ve) at the same level as the voltage at the base (Vb).
So clearly you are raising Vb to a potential that is high enough to turn the LED ON.
Try a circuit like this to read the GPIO input when your transistor base is touched:
simulate this circuit – Schematic created using CircuitLab
The idea here is that when an input is present on the base of the transistor, it will turn the transistor ON. When that happens current flows in the collector which will pull the GPIO pin LOW. Keep in mind that the collector current, Ic, is the base current Ib times the hfe value of the transistor. For most small-signal transistors hfe is in the 100s or even 1000s. So you get a sizeable collector current with very little base current.