Here is the internal block diagram of the 555.
On the left we can see a voltage divider as described earlier. The values of the resistors aren't relevant to this discussion, other than that they are all the same. That gives us 1/3 and 2/3 of Vcc at the points between resistors. The rest of the behaviour of the circuit is driven by this divider. One of the benefits of this is that the operation is independent of Vcc.
There is a bit of an urban legend that claims the 555 got it's name from these 3 resistors each being 5K. This is officially not true from what I have found from some research. In fact the part number "555" was arbitrary. See this interview.
Moving right we find two voltage comparitors. The top one compares the voltage on the threshold pin (6) with the 2/3 Vcc value. Then the threshold voltage is above 2/3 Vcc the output of the comparitor goes high. The lower comparitor compares the voltage on the trigger pin (2) to 1/3 Vcc. Note that the trigger input is connected to the comparitor input annotated with a negating circle. This indicates the input that should be lower that the other input for the comparitors output to be high. On the top comparitor the negating input was connected to the 2/3 Vcc voltage so the threshold value had to be the higher of the two for the comparitor output to be high. In the bottom comparitor the trigger voltage has to be below the 1/3 Vcc voltage for the comparitor output to be high.
Next we have the RS flipflop. The trigger comparitor output is used to set the flipflop (making its Q output high and, more importantly here, it's Q-bar output low. The threshold comparitor output is used to reset the flipflop, making the Q-bar output high. Notice that there is an active low (meaning that it is normally high and brought low to do something) reset pin (4) that can be used to reset the flipflop (and thus the 555) to a known state, with Q-bar high (which drives output low and discharge grounded, as we will see momentarily).
The Q-bar output of the flipflop is inverted and buffered (to be able to supply more current to whatever circuit is connected). This buffered signal is connected to the output pin (3).
The Q-bar output of the flipflop is also used to control a transistor switch that, when on, connects the discharge pin (7) to ground (when the not Q is high, i,e, when the flipflop is in the reset state).
Finally there is the control voltage pin (5) which can be used to override the operation of the voltage divider by setting the 2/3 point of the divider (the voltage that the threshold input is compared to) to an external voltage. Note that this also effects the voltage the input signal is compared to (it is now 1/2 of the control voltage)
As you can see this is a very simple and elegant circuit. The 555 doesn't do much other than compare some voltages (the divider and comparitors), keep some state (the flipflop), and ground a pin (the transistor). This is what makes it so versatile: with a few external components connected in various configurations, this little chip can do all manor of interesting and useful things.
We will be referring to the above diagram throughout the rest of this guide, so it's a good idea to have a pretty solid grasp on the material up to this point.
If you really want to understand the 555, you can grab the "Three-Fives" kit and poke around inside the circuit with an oscilloscope or multi-meter. It's a fully functional version of the 555 made from transistors and resistors, just like inside the real chip.