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TV writers, they often use "acid" as a kind of a shorthand for "wacky" -- they'll say something like "This sitcom, it'll be like Terry And June ON ACID! Imagine what that'll be like!" Yeah, I can imagine what that'll be like -- that'll be Terry examining the floral pattern on a plate for four days...
—Bill Bailey, Part Troll
Creative works are often hard to describe quickly and effectively, so writers often use comparisons or "They Fight Crime!" in order to get their point across. However, in recent years, it seems that despite constantly reminding us that Drugs Are Bad, the writers are beginning to develop a rather strong addiction to them.
This is a trope for works which are forever and eternally being described as being on some kind of mind-altering substance. The most common ones are crack (highly concentrated cocaine), acid (LSD), and steroids, but any drug can and will be used. Often used for Mind Screw stuff, but by no means exclusive to them.
The choice of drug can imply certain qualities. Works on speed are extremely energetic and fast-paced; works on crack are similar but with an element of surrealism or wackiness implied. Acid is more psychedelic and wacky, whereas works on steroids are usually bigger and more extreme. One would imagine a work "on NyQuil" would be dreamy and lethargic, while describing Show B as Show A "on [its] meds" implies that Show A is in some way weird, while Show B, while cut from the same cloth, is less-weird. Finally, a work on "angel dust" (PCP) would most likely be extremely violent, angry, or megalomaniacal in tone. These are anything but definitive, however.
Note that the chances are the creators weren't actually on drugs at all.
The name of this trope came from an American anti-drug commercial, where it showed an egg with the voice-over "This is your brain," then the egg being cracked on the side of a frying pan and the contents poured in, with the voice-over "This is your brain on drugs. Any questions?" This got so parodied that for a while people ordering eggs sunny side up would say, "I'll take a brain on drugs with toast," for example. (It might also explain why eggs over easy were so common for a while.)
Not to be confused with Made on Drugs.