That's funny, I had a similar question a few days ago: http://www.italki.com/question/261723. You omitted the first part without which the sentence makes no sense: "잔은 음료, 특히 물을 따라 마실 때 이용한다". So I would guess the sentence means: "A glass is used for pouring and drinking liquid beverages, especially water." But would be nice to get a confirmation from a native speaker of course :)

Oh, I didn't know 따르다 had this meaning. Thanks a lot, Marcel!

따르다 means "to pour" here and has nothing to do with "to follow" :D sorry I wasn't clear about that in my answer

Yeah, I guess one has the meaning of "according to, following to" and the other "to be different". But as far as I know, sometimes in sentence they can have different meanings too. In the sentence above I am not so sure what it wants to tell. My guess is that it puts water to a unique place among the other drinks. But 특히 is already used to do this job. I am a bit confused about why we need to use 따라 in this sentence. Thanks for the answer!

따라 comes from the verb 따르다, which is completely "different" from the verb 다르다.