There are some very long, technical white papers here and there that attempt to take a look at what you're referring to, but they are very dense reading and will make your eyes bulge by the second paragraph.
The essential influence boils down to the image below:
(https://forum.bottlehead.com/proxy.php?request=http%3A%2F%2Frichardsears1.files.wordpress.com%2F2011%2F06%2Ffigure-4-single-ended-signal-loops-with-ccr.jpg&hash=277a03c22f8d33b74ca02b2d95de2c9224674779)
The image shows a conventional single ended voltage amplifier. This is similar to what's in most of the commercial amps out there, and also is somewhat applicable to a basic driver stage as well. The red dashed lines and green dashed lines represent your AC signal current. The green line shows the input signal current, and the red line the resulting output. In each case, there is a capacitor (or two) intersecting with those loops (the capacitors are denoted C1/C2).
Where the signal current passes through a capacitor, the quality of the capacitor will become very important. In Bottlehead kits, Parallel Feed topology is employed, and one positive outcome is that the size of the final capacitor for a power amp shrinks considerably, allowing for a higher quality cap to be used (see left side image below).
(https://forum.bottlehead.com/proxy.php?request=http%3A%2F%2Frichardsears1.files.wordpress.com%2F2011%2F06%2Ffigure-5-se-para-and-direct-feed-with-ccr.jpg&hash=5ef815b3ec5bbbfe5a70b3671e1e965beb1faa86)
Additionally, there are often two amplification stages stuck together, and often times you will see a capacitor between them to block DC voltage, this is referred to as a coupling capacitor, and occupies a similar position as the capacitor in a parallel feed arrangement.
As far as why certain capacitors sound better than others, that becomes a hard question to answer. The preference for film type capacitors over electrolytic capacitors can be boiled down to chemistry and measurement, but what makes one metalized polypropylene capacitor sound better than another metalized polypropylene capacitor can be quite elusive. For more reading on this, you can check out this capacitor shootout:
http://www.laventure.net/tourist/caps.htm From my personal perspective, I shoot for film and foil capacitors whenever possible (imagine long stacks of alternating metal foil and plastic film rolled up and stuffed into a tube). Next down the list are the metalized capacitors (imagine depositing a very thin layer of metal onto a layer of plastic, then rolling that up), with polypropylene as the best film material. Last up would be electrolytic capacitors, though there are times where they must be used, and certain electrolytic capacitors exist that perform quite well.
Feel free to request more specific info. Hopefully this thread doesn't become "my favorite capacitor is XYZ".
