Q:

What is "crimping"?

In "The Mighty Boosh", Vince Noir (Noel Fielding) and Howard Moon (Julian Barratt) have developed a kind of vocal play in which they seemingly talk rhythmic gibberish in an a cappella style. I'm not understanding how they're building up the structure of these "crimps" nor what the subjects of most these individual crimps is meant to be.
What exactly is "crimping"?

A:

From the Urban Dictionary:
A form of scat singing usually performed as a duo. First invented and developed by Vince Noir and Howard Moon. Often Characterized by lines of interconnecting verse usually referencing abstract imagery, concepts and characters.
Crimping refers to a fictional type of song which usually contains no particular musical element but is instead sung acapella, does not follow any single tune and contains surreal lyrics that often make little sense. Other common characteristics of crimping are unusual subject matter such as soup or jackets, repetition of vocal lines and dance gestures to accompany the songs. The style is reminiscent of scat singing.
Crimping originated in the British BBC Three series The Mighty Boosh where the two main characters, Howard Moon (Julian Barratt) and Vince Noir (Noel Fielding) sing a song with each other, often for nostalgic purposes. The most obvious of these is "The Soup Song", with "Calm A Llama Down" and "Jean-Claude Jaquettie" also being prominent examples.
These small tunes were not known as crimping until the third episode of the third series, "The Power of the Crimp", in which the main characters stage a "crimp-off" against their doppelgänger rivals, The Flighty Zeus. The match culminates in a four-way crimp to which both Bollo and Naboo contribute.

