I saw this question on another SE site, What is meant by "them hats" in this context? I hear the use of "them [word]" many times, does it mean like their or these? or what exactly?
In this context, it means those hats. The phrase "how about them [objects]" is deliberately wrong for humor value. The construction is used deliberately in the meta posts about hats because the mods on each site want everyone to know that the hats are supposed to be fun. Consider a correctly formed sentence:
Aren't those [objects] remarkable? Let's talk about them.
It's correct and clear, but it's not really humorous. The implication of such a sentence would be "I want to have a serious discussion about this." This would be an appropriate way of discussing the cherry blossoms or a military band.
How 'bout them [objects]?
The use of deliberately wrong syntax indicates that the speaker wants to have a "fun" conversation about the objects, or at least an informal one. One of the most common contexts for the phrase is:
How 'bout them Cowboys?*
Or, combined with another non-standard usage to convey the informality more fully (as noted by J.R.):
How 'bout 'dem Bears?*
In this context it means something like: "I saw [the named sports team] play last night and they were awesome! AGREE WITH ME!"
There's a related use of this phrasing in a sports context. When speaking to fans of one sports team or another, using the phrase in reference to another team can be considered an insult. (Mild or severe, depending on the relationship between the two people speaking.) In that context it's a statement like: "Hey, my team is better!"
*Disclaimer: I am agnostic toward American football. No endorsement of or insult to the Cowboys is implied. They were chosen because the sentence flows nicely around their name. The Bears, well, they're the Bears. I put them in only because J.R. used them for context.