the astable multivibrator

An astable multivibrator is a circuit with no resting state: it never settles, but flips its output high, then low, then high again, forever, all on its own. The word astable means not stable in either state. It is the free-running square-wave mode of a relaxation oscillator (and the most common way to use a 555 timer). Think of it as a metronome you cannot stop: power it up and it just keeps ticking out a square wave.

In a 555 wired as an astable, the capacitor charges up through two resistors (call them Ra and Rb) and discharges through just one (Rb), because the discharge pin sits between them. So charging is slower than discharging, and the output spends longer high than low. The output is high for a time of about 0.693 times (Ra plus Rb) times C, and low for about 0.693 times Rb times C, where 0.693 is the natural logarithm of 2, coming from charging across the one-third-to-two-thirds threshold gap. The frequency is f equals 1.44 over ((Ra plus 2 times Rb) times C). For example Ra equal to 1 kilohm, Rb equal to 10 kilohm, C equal to 10 microfarad gives about 6.8 Hz, a gentle blink.

Astable mode is how you make blinkers, tones, clocks, and the carrier for simple PWM. The honest catch in the basic 555 astable is that because charge goes through Ra plus Rb but discharge only through Rb, you can never quite reach a 50 percent duty cycle (equal high and low times); the high time always exceeds the low time. To get a true square wave you either make Ra small and Rb large (approaching but not reaching 50 percent), or add a diode so charge and discharge take separate paths, or use a different topology. As with any relaxation oscillator, the frequency is only as accurate as your resistors and capacitor.