Electret mics contain a FET or other transistor that acts like a tiny preamp, it IS possible to feed a small power amp such as a 386 with just an electret mic.
Most of the time pre-amps and power amps are used in combination because of how transistor amplifiers work. The two commonly used types of transistor amplifiers are common emitter and common collector (also known as emitter-follower). Common emitter amplifiers produce a voltage gain, but no current gain (they also invert the signal, which is of no consequence for audio), so are very poor choices to drive a speaker or other load, but make great preamps. Common collector amplifiers have the opposite trait. They will produce a current gain, but the voltage remains the same (actually there is a tiny bit of voltage loss, but it can be ignored in most cases. Also, they won't invert the signal). In combination, a common emitter amp feeding a common collector amp produces a very large gain in power.
When considering IC's, virtually all of your Op-Amps will act as preamps, and you will need a power amp to follow it up for driving a load such as a speaker.
Edit: Yes, electret mics DO need power. Typically you'll see a resistor and cap on the positive lead of an electret mic. The resistor supplies the mic with the proper voltage and the cap blocks this supply voltage from the input of your amplifier while passing the audio signal through it.