What is a Carry?

Let's cut all the unnecessary babble out as early as possible:

1. Ye, I'm probably gonna whine about something.
2. It's probably about not being able to carry.
3. I'd like to know what exactly I can do to change that.

Long story short, like many people at low Elo, I'm frustrated. Frustrated that sure, I have bad games - sure, I have great games (I mean let's get this out of the way first of all, I'm currently Bronze 1, was at peak Silver 4 last season) - but here and there, what frustrates me most are those matches that are almost literally (at least in my eyes) impossible to carry.

EDIT: (Bronze 1 my first season, made it to S4 3-4 times and was struck with loss streaks every time. Ended S5. Won 8 of 10 Promos and was placed into B1 this season)

My latest, most frustrating example? 16/4/4 on the Donger. The team kept getting caught out in the jungle (where, mind you, they had no vision/wards placed). Whenever we had good engages, they didn't translate into objectives taken (my biggest peeve). One particular engage was especially humorous, because after taking a successful engage, the adc and mid laner decided to farm up in the enemy jungle instead of taking two perfectly pushed in Tier 2 turrets. They overstayed their welcome and were deleted shortly after while still in the enemy jungle. I even did my best to shut down the Nasus I counter picked Heimer into (yes, I was counting on shutting him down early enough so he wouldn't farm my turrets, and it worked) early on with 3 kills before my first death. Even then, better team was better, GG [Defeated screen rolls through]. That was in Promos, of course.

Sigh, perhaps it's just the luck of the draw. Perhaps I truly am Bronze 1 material, but (maybe it's not an effective reference) according to lol.arenaonline.com the only thing I don't lead most other Bronze players in is my win rate, GPM(less than 3 gold below most Bronze players), and Avg Gold by 20 mins (less than 30 gold below most Bronze players), AND EVEN THEN, it's marginal (see link provided for reference).

So, WHAT is a carry, really? HOW do you do it? In a game that revolves almost entirely around team mechanics, how is it that I am consistently placed with people who simply don't understand those basics we all learn to love? Upgrade your wards. Don't push without ample vision. Help snowballing lanes if/when possible. Win an engage? Take an objective of some kind, even if there's only time to clear the enemy jungle and back. Something is something. DON'T OVERSTAY YOUR WELCOME, keep track of death timers. Keep your eye on your minimap. Etc. Etc, I could go on and on, as we all know.

Sorry, perhaps this was more of a rant than a cry for help. In any and all cases, I really do want to get better, because I feel like I don't belong in Bronze, in the least. Sure I might not even be gold material yet, but I can't be cursed to suffer teammates of Bronze quality for so long and not be rewarded, even if it is simply with community help. So please, any feedback would be greatly appreciated.

PS. I've even taken these other things to heart to try and help my team's and my performance in-game, to little effect at times (Credit here goes to Riot for the Loading Screen Tips):

Teammates perform worse if you harass them after a mistake. Challenge others to be more sportsmanlike. Players who cooperate with their team win 31% more games. Players who verbally abuse their teammates lose 16% more games. Players who curse at their teammates lose 13% more games. Players perform better if you give them constructive feedback after a mistake.