Constructed languages add to the flavour of a world to build.
There is now a dedicated stackexchange for constructed languages in public beta here
Go forth and visit it!
I just want to make a couple of notes, as someone who participated a bit (though mostly lurked) during the Constructed Languages private beta:
First, Constructed Languages has so far taken a focus more towards preexisting-existing languages. Those types of questions are a bit like how on Worldbuilding, we allow questions about preexisting works. The thing is, Constructed Languages leans pretty heavily in that direction and away from questions about languages constructed by users. It's not a problem, certainly, but it is something to think about.
I also think that Constructed Languages is going through the growing pains of having subjective questions (which encompass many of them I'm-making-my-own-conlang questions). There's a fine line to be drawn. I think we've drawn it (and erased it, and redrawn it, a couple times) on Worldbuilding, but Constructed Languages still has to flesh that out a bit.
Finally, I'd like to add that I don't think we have a huge amount of folks with backgrounds in linguistics on Worldbuilding; there's certainly a number of people on Constructed Languages with that background - some first-time Stack Exchange users. I hope there's a bit of cross-pollination between the two sites. Both are going to get conlang questions, and if there are people out there who can write great answers, I hope they see us here on Worldbuilding.
A little reminder:
Questions about worlds with constructed languages are still on topic here.
Pointing users to conlang stack is all good and fine, and asking them to rethink which site would be better for their question is OK, but nothing has changed in voting to close reasons. Questions we would allow here before are allowed here now.