Both Spider-Ham and Spider-Man Noir, were created as different versions of Spider-Man, specifically Peter Parker. Spider-Ham as comedic cartoon pig, and Spider-Man Noir a gritty pulp detective. The two had no interaction till the Spider-Verse event, but had no significant interactions. They also both appeared in the Ultimate Spider-Man tv series version of the Spider-Verse event, but had no interactions there as well.
Spider-Man: Into the Spider-Verse (2018)
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The ship rose after the release of Spider-Man: Into the Spider-Verse. Fans will typically ship it as a crack pairing, and enjoy having fun with pairing. Typically drawing the two in more comedic situations or more relaxed one. A rubix cube is involved a lot of the time.
Shippers will often compare the ship to Jessica and Roger Rabbit from the movie Who Framed Roger Rabbit, as that was a movie with a human/anthropomorphic animal relationship. It's also a relationship that has an extreme height difference, as well as similarly opposite personalities.
There are some shippers who are uncomfortable with the animal/human aspect but still like the idea. Many of them instead will ship Noir with his universe's version of John Mulaney, given that John Mulaney voices Spider-Ham in Into the Spider-Verse. This also led to art and manips of John Mulaney stand up bits being said by Spider-Ham.
On AO3, HamNoir is the most written ship for both Spider-Ham and Spider-Man Noir. It's also the third most written ship in the Spider-Man: Into the Spider-Verse tag.