I do like playing the occasional Urgot for fun but when I have the opportunity in champ select I feel very awkward. I'm not exactly sure what part of the team composition I'm covering. If I'm mid, then we probably won't have an AP carry so the enemy team can armor build. If I'm bot "adc" I've gimped us in damage output as the enemy team probably has a real ADC. I'm not a support and I'm not a jungler. I guess I'm covering the bruiser role as Urgot is usually off-tanky? I know the general LoL community doesn't realize the utility Urgot brings so they don't plan their champion choices accordingly (like picking Swain, Vlad or Kennen for top if I'm mid) so how should I best advise my teammates about my function on our team?

He can fit into certain areas but you're contrasting two things. Trying to fit someone with no place in the current meta into a current meta lane. It is sadly a very rough place for many people and champs.

ADC that fit well into the current meta are those with good high ADC damage but also have escapes. IE. graves, corki, ez and even the likes of vayne and what not.

When it comes to a bruiser he can always fit that role sure but hes not gonna escape from anything really, he does have a slow on his missle if your shield is up but with a lack of sustain and low movement speed and late game fall out then you are missing out on a huge deal of utility because a brusier in the current meta will usually be pretty solid at protecting his adc and still sustaining and presenting a threat. IE. Jayce, Darius, Shen, Cho, Lee... etc

This is just my opinion and what I have seen/learned from solo as well as group play and in watching others play so perhaps I am not 100% on point about all this but I do believe most of it i fairly accurate.