Before we can understand much about the operation of the 555 we need to understand resistor-capacitor circuits, commonly called rc circuits.
Resistors resist the flow of electrons through them. Capacitors store electrons. That's about it. If we place a voltage across a resistor a current (i.e. a flow of electrons) will flow through it. The greater the voltage, the greater the current. The greater the value of the resistor (it's resistance) the lower the current.
Things get interesting when we put resistor and capacitors together. You'll find them working together in various ways in all kinds of circuits. For the purpose of this guide, we're interested in a specific way of combining them.
Consider this simple circuit.
If C is fully discharged (i.e. is empty) when the power is applied, the voltage V will be 0 and C will start to charge through R. As it charges, V will increase. As this happens the voltage across R will get smaller. In turn this will lower the current flowing through it and this will slow the charging of C. In fact, V will follow a well defined logarithmic curve.
Similarly, if we now connect the top end of R to ground instead of Vcc, C will discharge and V will go back to 0, again on a logarithmic curve.
The timing of C's charging and discharging (and V) is dependent on the values of R and C. If we make the value of C larger it will charge more slowly. Likewise if we make the value of R larger.
This might make more sense if we use an analogy. Let's represent C by a swimming pool and R by a hose. If we try filling an Olympic swimming pool using a garden hose it will take a long time. If we make the pool smaller by replacing it with a kiddie wading pool (i.e. a lower capacitance) or the hose bigger by replacing it with a fire hose (a lower resistance) it won't take as long to fill.
When we have a circuit like this a handy number is the RC time constant. The value of C in farads multiplied by the value of R in ohms yields the RC time constant in seconds. For example the RC time constant of a 1k ohm resistor and a 1 microfarad capacitor is:
1000 ohms * 0.000001 farads = 0.001 seconds, i.e. 1 mS
As mentioned, the charging of the capacitor follows a logarithmic curve rather than a linear, so the rate of charger/discharge changes over time. The RC time constant is quite handy. V will be within 1% of Vcc in 5RC seconds. Furthermore, it will be at 63% of Vcc in RC seconds. The usefulness of this will become apparent later.