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1.
A "56k Warning" is a nice way of telling someone they might stand a chance of a black hole opening up inside of their home if they use dialup and try to access a site bogged down with images or videos.

Basically if you're in that 16% of people who use dialup, you need to watch out for these.
DSL / Cable: HAHAHA! These videos have such a high comedic value. I'm going to post them.

Dialup: Hey! Videos with comedic values?! I want to see! *Clicks*

Dialup: Oh noes! I ignored the 56k warning CLEARLY posted!

*Black hole opens up and sucks out the persons living room*

DSL / Cable: lol?
by Da Milkman May 24, 2009
 
2.
An internetism that would warn users that what ever they were going to open would slow down their connection, such as a ton of pictures. However, since only 10% of Americans use dial up anymore, the term is of a general use to prenote that there is going to be a lot of content.
Thread title: "Jessica Alba vs. Jessica Biel (56k warning!)"
by Agamemnon582bc September 04, 2008