This can be both in-universe (like word origins that say something interesting about the society in which the conlang is canonically spoken), out-of-universe (like little hidden references you wouldn't expect people to notice), or even both.
I could mention a million things in my own conlang, but the example that inspired this post was the slang term "3-zo" or "poeezo" /pøːzo/ which basically means "a recurring expense; a person, form, or notice sent for the purpose of extracting this money; or the money so extracted". And this word "3-zo" comes from a clipping of yaPoeezolloeyya /japøːzoʎ.ʎøj.ja/ literally meaning basically "the three animals" — and referring to a set of three institutions that work together to help the rich and hurt the masses.
And this idea of "three animals" taking money from the poor was inspired by the Occitan folk song "Ai vist lo lop", where the description of a wolf, fox, and hare dancing around a tree is commonly taken as a metaphor for the monarchy, nobility, and clergy engaging in various merriment, while the peasants get screwed over. That folk song also describes how the peasants toil year-round to earn "a few coins", only to find that all their money is squandered within a month.
So yeah, my conlang's word for like "rent" and "taxman" and "utility bill" and "Netflix subscription" is ultimately in reference to an Occitan folk song about dancing woodland creatures.