The option doesn't have any effect on players what so ever (Riot has said this multiple times). If I report you for unskilled, your mmr doesn't get hit, you don't get banned.
What it does do is tell Riot that they have a problem with their matchmaking system.
Let me give you an example. I'm ranked Plat II right now in solo queue. According to op gg, that puts me in the top 3% of the NA ranked player base. Last night I had teammates that didn't know how to play the game League of Legends. Meaning, they didn't know how to play their role, use their champion's abilities, or even build reasonable items. These are the players that will all in their lane opponent at 2 mins and give up first blood, then blame their jungler for not being their to help them (most junglers finish their 3rd buff ~3mins or so). A few of these guys will go on to give up 10 deaths by 20 mins due to overextending, lag, or a number of other factors making them look like complete imbeciles.
I will report these guys for unskilled every time because I don't think it's fair for them to be matched against players that clearly outclass them. Personally, I don't care, I will carry whoever. But when the player feeds 10 deaths, rages at jungler for "losing their lane", and then quits the game, that can't be a good experience for them. The matchmaking engine is supposed to match me with 9 other players of "equal skill" so I will definitely give feedback if it is not doing its job correctly.
So I vote them unskilled. Nothing personal, just helping Riot get their shit together.
Maybe it's just one bad game. If so, whatever. My one vote of unskilled won't even make Riot blink. But when my peers are all pointing out that something is going on, that points out to Riot that they either have a boosted account, or a bug in their matchmaking algorithm, or something else going on that's ruining the play experience for 10 people in each game. I hope my teammates are also reporting me if they feel that I played poorly as well (and I do make mistakes, everyone does). Because that's how the system gains feedback to fix itself.
Here's a video of the day from my twitch stream last night. This is my second time this season getting promoted to plat I and my first few games up there. Take a watch and see if you agree with me on the players I voted unskilled. My stream viewers were also commenting that they thought a few people were boosted based on how they were playing (But could just be one bad game!).
5 hour solo queue session at 0 lp in Plat I:
http://www.twitch.tv/gundaymonday/b/625396568
(My criteria for unskilled = poor map awareness, poor mechanics, unnecessary deaths, or blaming your teammates for your own mistakes in chat)