When listening to air traffic control (ATC) communications on something like LiveATC there is a lot of feedback/static that often makes it difficult to hear. Do controllers hear the same feedback and static in the tower or is this due to the receivers used to "listen" to ATC frequencies?
The real quality is almost always better, and I'll give a simplified explanation for why.
LiveATC works by an individual volunteering to host a receiver on their house. Aircraft use VHF radio (except in remote and oceanic areas). VHF radio waves can only travel in line-of-sight. Therefore, if the person's house cannot see the aircraft (which given the sheer distances involved is common), the audio received will be of poor quality, with lots of static, and sometimes even unreadable.
But real ATC doesn't use just one receiver - there is a whole network of receivers and transmitters, in strategically placed locations. This means that no matter where the aircraft is, it will be within line-of-sight to one of them (except for in remote and oceanic areas, where HF radio or data-link is used).
Sometimes one ATC frequency covers a massive part of the world. When I'm flying in these areas, I can hear ATC clear as day but can't make out the aircraft they're talking to because they are hundreds of miles from me, and my aircraft receiver can't see them.
Of course, sometimes the radio from an aircraft is just terrible thanks to poor equipment or excessive cockpit noise. But in general what you hear on LiveATC is much worse than what the controllers are hearing.
In my experience in both an ARTCC and TRACON, the majority of radio communications were clear and without noteworthy feedback or static. There were some exceptions that were likely the result of a poor quality transmitter/headset/microphone from the aircraft and/or its location (low altitude, mountainous terrain, etc.).
Typically, considering the exceptions noted above, high quality avionics in commercial/business aircraft (and the majority of General Aviation aircraft) and the quality and positioning of ground receivers normally results in excellent radio communication from the ATC side.
Short version: Poor quality audio on LiveATC is mostly due to obstructions attenuating the signal. Controllers and pilots usually don't have much trouble hearing each other unless there are multiple stations transmitting on the same frequency at once or there's something like a mountain in the way (or possibly a building in the case of airplanes on the ground.)
A couple of other answers have hit on the problem here a bit, but the reason isn't that ATC has multiple transmitters and receivers. Indeed, most ATC frequencies have just one antenna, as a controller has noted in the comments. More than one transmitter on the same frequency causes problems, in that the signals will interfere with each other and that interference will vary depending on the location of the receiver, so multiple transmitters on the same frequency aren't (intentionally) used much.
The audio as heard by pilots and controllers is indeed generally much better, but it's not usually due to some complex network of transmitters for the same frequency or even entirely just due to better equipment (though the latter certainly helps.) The main reason for the difference is line-of-sight.
The VHF signals used primarily for aviation radios generally have poor penetration of, well, pretty much everything except for the atmosphere. Conveniently for ATC and pilots, controllers and pilots (or pilots and other pilots) who are talking to each other are usually either on the ground at the same airport or one or both are in the air.
Stations that are both at the same airport usually don't have much blocking their signals to each other. The transmitters are strong enough that they can typically overcome whatever few obstacles may exist on the field and ATC's antennas are generally placed so as to minimize obstructions between those antennas and where airplanes will normally be on the field.
When an aircraft is in the air, it's usually up above any nearby trees and buildings within a matter of seconds from leaving the runway. So, when it's not in the immediate vicinity of the airport where ATC's antennas are, it's up high enough that it has clear line-of-sight to them anyway. Once you get above the treeline (or roofline, as the case may be,) line-of-sight distance increases extremely rapidly. Even from only a few thousand feet up, you can see the ground 100 miles away on a clear day and aircraft in flight from even farther (if they're even big/well lit enough to see from that distance.) Even while just putting around at 1,000 feet above ground level in the pattern of an uncontrolled airport, I can usually hear traffic in the patterns of airports 100+ miles away that use the same common traffic advisory frequency.
Where the problem comes in with LiveATC is that its receivers are on the ground and generally not actually at the airport (or ARTCC, etc.) Thus, any obstructions on the ground between the receiver and the airport will be attenuating the signal received from either ATC or airplanes on the ground. Hills, mountains, and buildings near the receiver can also attenuate the signal between the receiver and aircraft in flight. This is especially true if the receiver is in a densely-populated area, as areas near major airports often are. The antennas that ATC uses at the airport are usually out in relatively wide-open parts of the airfield. LiveATC receivers, however, usually aren't in the middle of a big open field like that. And they also usually don't have as large or high-quality of antennas. Additionally, the antennas are likely indoors rather than mounted outdoors, resulting in signal attenuation from the structure in which the antenna is located.
ATC antenna placement and frequency assignment go through an extensive analysis process that looks at the targeted airspace volume to ensure satisfactory radio coverage. The analysis also looks at where the frequency is used elsewhere to prevent any type of interference. The study looks at the altitude of the aircraft in the airspace volume, the length/width of the sector, and the terrain (flat vs mountainous).
When John Doe decides to host a LiveATC receiver at Wayoutintheboondocks, ND, none of this occurs and audio quality can suffer.
One additional cause for the low audio quality is the audio bitrate that LiveATC uses to record and broadcast their audio. The audio is typically 16 KHz which is just fine for spoken word audio, but the MP3 bitrate is around 17 Kbps. Your typical music service will use an audio bitrate at or above 128 Kbps. At ~17 Kbps there's just not a lot of data there, so audio quality suffers.