When audio is intentionally distorted to sound as though it's extremely loud. Like, speaker-destroyingly loud. Ear-damagingly loud. And yet...not loud. Because, you see, the volume hasn't actually changed. It's Fake Loud. Basically, anytime you want to the listener to understand "this is loud" without actually, you know, deafening them.
When it's portrayed, fake loudness might actually be mixed at the same volume as other elements in the music/audio. But since it's meant to convey extreme loudness, various distortions are used to emulate this. This can include: reverb effects (to simulate vast echoes), sudden tinniness to the sound (as if the speaker's been blown out), crackling, digital squelching, white noise, high-pitched ringing, or a subtle/complete deafening of other sounds in the mix. Can also be achieved by severely clipping the audio levels for a rawer sound, or, when recording, muffling the sound.
An auditory trope. In music, used purely for cool.
Related the Loudness War, which contributes to this as its heavy compression of the dynamic range can make this the only way to represent a sound as louder than its surroundings, since the entire soundtrack is already as loud as the signal can support.
Also related to Steel Eardrums, as it's more believable for the characters not to be deafened by having unprotected ears exposed to gunfire when the viewers themselves are not subjected to an actual volume spike.
Stage Whisper is a dialogue-specific inversion, where characters are supposedly speaking quietly but are loud enough for the audience's benefit.
- "Gutter" by Paper Route features a distored and explosive bass tone that crackles as if it's being digitally clipped.
- "Mushrooms" by Xzibit is similar; after a gunshot at the end, Xzibit's voice is muffled and there's a high-pitched ringing noise.
- "Halfway Home" by Blackalicious and DJ Shadow intentionally cranks the reverb up to distorted and deafening levels, making the music sound like it was recorded using a cheap microphone at a live concert (which is contrasted nicely against the vocalist's perfectly normal and studio-quality vocals)..
- The Ringwraiths in The Lord of the Rings movies. According to the commentaries, they worked very hard to make the scream sound loud without actually being loud.
- The D-City Rock music video from episode 10 of Panty & Stocking with Garterbelt. 
- Our Man Flint. Flint turns up the volume on an enemy mook's headphones. The audience hears the intense noise as a hideous screeching.
- The band Sleigh Bells practically runs on this, with nearly every song featuring heavy distortion on every element in the song and raw production.
- A lot of popular electronic music has been doing this, ever since Justice released their excessively distorted debut album in 2007. Skrillex is a modern main offender. Some of these efforts have perpetuated the Loudness War.
- A popular effect in modern dance music is known as sidechain compression. In a nutshell, it uses one sound (like a kick drum) to affect the volume of another sound (like the chords), giving it that distinctive pumping sound and making the kick drum sound a lot louder than it is.
- Before this, intentional distortions in music were used as far back as the 60s. Jimi Hendrix's famed distortion came from live concerts, where only the vocals would be broadcast over the concert's PA system and the instruments would come out of amplifiers. As a result, the amplifiers had to be turned Up to Eleven just to get the guitar as loud as his voice, resulting in the distinctive fuzzy overdrive tone.
- Rock groups such as Sonic Youth, Velvet Underground and guitarist Robert Fripp, as well as countless industrial acts from The '80s onwards, have used plenty of Fake Loud noises and textures. For example, Primal Scream's "Accelerator" off the album XTRMNTR, while generally mixed at the same volume as the rest of the album, is intentionally extremely distorted to the point where the listener can't even hear the drums.
- As The Veneer Of Democracy Starts To Fade by Mark Stewart & The Maffia. Prior to the recording, Stewart had been going to Dub Soundsystems (which deliberately play at ear splitting levels) and bootlegging them with a cheap cassette recorder so he could relive the memories at home. He liked the effect so much he had the engineer produce the whole album like that. It's hard to explain, but there's a discernible difference between turning everything up very loud in the studio and a live bootleg of an incredably loud performance done on cheap equipment, and the engineer managed to capture it perfectly. Even down to the particular quirks caused by Soundsystems often working with rudimentary mixing equipment and the amateur engineers/DJ's not quite understanding how everything works/being too messed up to care. The only part that gives it away is some of the panning, which would be impossible to capture in the way it's pretending, but it sounds cool so why not? They genuinely went to extraordinary levels to make the album sound as terrible as possible.
- Occurs in the last part of mpn1990's review of Action 52, when he has a fit of screaming angrish.