Could some one explain to me how my circuit works? I accidentally hooked this up while trying to work out an amplifier. I'm thinking there's something like RC resonance going on, but I'm not sure. Please help? Thanks.
Maybe your circuit is rather amplifing than generating an oscillation.
This can happen if the "unconnected" base is picking up some stray fields (e.g. radio signal or fields generated by a switching power supply, etc.)
Since you are using a solderless breadboard, the base is probably connected to a line than can act as an antenna.
More information needed.
Given what we know, here is a COULD happen.
Base leakage charging base stray capacitance could turn transistor on - how hard depends on leakage.
(1) Low collector may provide a discharge path or the speaker indictor and capacitor resonance may drive collector under ground so that CB diode forward biases and discharges base capacitance and allows cycle to restart.
(2). If there is CE leakage this is a classic brounded base amplifier without the base grounded :-). Emitter is input. Collector is output. Positive in phase feedback occurs c to e of transistor. Capacitance between strips on plug in solder board MAY be enough. Base would need a whisper of fwd bias - depends on construction. Leakage alone MAY be enough.
What transistor is used?
This is possibly somewhat like an informal Colpitts Oscillator.