Understanding the reasoning behind the "meta" will let you be more successful in "breaking it"
The meta. It's a nebulous concept that hangs over league and govern's how the game is play. It's laws, enforced by habit and by player interaction, provide a very real service to the community. Without them the game would be chaotic, you would not be able to teach a new player any sort of structure. Take the meta away and you have a game of 5v5 with 3 lanes and two Nexis. It can be quite daunting to take all this in. What do I pick from 117 champions? Where do I go? What do I do for the team? These are all questions that would have to answered every single game. The meta provides the answers in a quick, concise, easy to teach way. Mid is for Assassins and mages so they can roam, you provide burst and AoE damage. Top is for tanks, fighters, and close in mages, you provide utility and CC. Jungle is for bruisers who can pressure the entire map and provide initiation and utility. Bottom lane is for the ADC who is all about raw DPS and a support who fills in the team's gaps and protect's the ADC.
More often then not "Breaking The Meta" get's construed as "I want to play this champion in this role, I don't care what I'm supposed to do in that role, that's just meta". The Meta is this arbitrary rule to be fought against, why should it dictate how I play? Don't look at it as a rule, look at it as a guide. The Meta is simply a construct to guide an undisciplined group of 5 strangers into some coherence. It spells out quite effectively what is desired in a good team. You want to play Annie ADC? As long as you understand the responsibilities you face, the role you've chosen, and why you're going to a lane then that's fine. But to simply pick it without thought is asking for disaster. You might get a few wins on unsuspecting targets, there is a pretty big honey-moon with most off meta picks I notice before you run into someone with a better understanding of the game.
You want to take Vayne or Quinn top? Think beyond the lane phase. Is your goal just to win lane then figure it out from there? What is a team fight late game going to look like if you have 2 adc's and no front line? What if you don't get fed? It's a cost benefit that requires you to look beyond you're own wants and your own lane. Understanding the underlying reasons for the meta in the first place better informs you of your pick's strengths and downsides. So don't ignore it as some rule to be broken. Instead learn it, why it exists, and then use that knowledge to find your place in it with your Annie adc.
EDIT: I've seen a lot of good discussion both here and on reddit. I guess a good TL;DR for the whole thread is: "Think about what you're doing, and why you're doing it. Learn the fundemental reasons why the game is the way it is, and use those reasons to shape your actions and character choices. Independence of Thought is a powerful thing, but it can lead to hubris. Always be critical and analyze how and why things work and why they failed. Then and only then can you reach true enlightenment. En taro tassadar, so say we all, may the force be with you, live long and prosper, whoa, see you space cowboy.... etc... etc...