https://www.reddit.com/r/196/comments/17ee71i/why_is_this_sub_called_196_what_is_the_lore_about/

195 was a similar meme sub with the same rule, created by friends who lived in apartment 195. Eventually it shut down due to only having one active mod and becoming pretty popular, to the point it was too much effort to keep it going. It shut down 420 weeks after creation, nice.

196 was created to carry on the sub

The 420 weeks thing might not be just a coincidence though as implied- someone else added:

the main concept was that the sub was gonna be shut down after 420 weeks