A circuit like this is designed to do three things:
First, the AC signal passes through a transformer. Transformers are inductors with a special coil winding which allows the AC signal to either be multiplied, or reduced. Thus you can "step-up" or "step-down" the signal. However, transformers provide one more very important thing - isolation. Since a transformer is actually an inductor, there is no physically connection for the AC current to flow between the input coils and the output coils. This is a safety feature for both people and the electronics, as it keeps the circuit from unloading constantly, in the case of a short.
The input signal looks something like this... a lot of imagination really comes into play here, since it's sort of hard to show with ASCII (also note, the peaks would be rounded, not triangular):
/\--/\--/\--/
--\/--\/--\/--\/
Second, it takes an AC input (sine wave) and evens it off into a DC output (square wave, or a "line" in this case). The rectifier is responsible for letting only the correct cycles of the AC current through (for example, only the positive cycles), thus eliminating the "valleys" between the "hills."
The resulting signal:
/\_/\_/\_/\_/
Finally, the filter capacitors charge with the remaining current, and discharge, evening out the gaps between the voltage peeks. Depending on how "dirty" the signal can be, the circuit may use many filters, or no filters at all. If you have an electronic device that's giving out a lot of static, noise, or other garbage, the problem is often these filter capacitors in the power supply (though things like radios also use tuning capacitors, are subject to loss of signal quality over distance, etc. - it gets messy).
Again, imagination is needed, but the result looks something like:
/-\_/-\_/-\_/-\ (dirty)
/-\-/-\-/-\-/-\ (cleaner)
----------------- (cleanest)
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