Would you help me understand this simple circuit?
It's common-base. You can recognize it because the base is bypassed with large value capacitor to a supply rail or ground (it's at AC ground). Large is in relation to the operation frequency, which in this case appears to be about 100MHz. 
C1 keeps the base grounded for RF, R1 provides bias when the input is open (or capacitively coupled).  
L1 and C2 + C3 + Ccb are a resonant circuit. The output is taken from the collector. C3 provides feedback to the emitter, around half the voltage at the collector appears at the emitter. Without C3 it won't oscillate, or at least not very well. C2 allows the oscillation frequency to be determined separately from the amount of feedback.