The output capacitors are because the 7805 can only supply a limited peak output current (average or transient) whereas a capacitor is only limited by its internal resistance. For instance, an electrolytic capacitor might have an effective series resistance of 1 ohm and when connected across a 5V supply, clearly the peak current it can supply will be about 5A - this is much bigger than what the 7805 can supply BUT remember we are talking transient demands not average demands by the load.
As a footnote, it's always best to put a capacitor like this where it is needed - at the point of load because transients of several amps up and down long copper traces can cause other problems.
The circuit you posted doesn't show a particularly important capacitor this being the input cap to the 7805: -
Note the 0.33uF cap shown at the input - if you have long feed-wires connecting the power to the 7805, a capacitor helps peak demands taken by the 7805 - this is because feed-wire has inductance and the capacitor prevents instabilities.
The LT1528 is typical of some "adjustable" voltage regulators - the output can be set by a potential divider from output pin to the feedback/sense pin. Normally the LT1528 runs at 3.3V on the output and the sense pin can help the 3.3V be reproduced at some distance from the regulator (say close to a load). If you look at page 1 of the datasheet it shows you various settings for these resistors that allow an output greater than 3.3V.
This is certainly a technique I have used a few times to overcome the limited power dissipation abilities of the diminutive 78L05. I've known the range of currents that the load is taking and placed a dropper resistor in series with the power feed to the device.
Why didn't I use a switching regulator?
I couldn't - I was sending power and data down a 50 m cable (phantom power) and the extreme complication of filtering out the switching regulator's current surges meant it just wasn't feasible.