If your Matchmaking Rating is higher than that of the players in our league, you'll get more league points for winning and lose less for losing.
If your Matchmaking Rating is lower than that of the players in your league, you'll lose more points for losing and get less for winning.
The Matchmaking Rating, not your position in the league, determines with whom and against whom you'll play.
In other words, Matchmaking Rating is your genuine rating, and it influences your position in the league, though it's not directly connected with it. You can be rated higher than your league and play against players of a higher league than yours, and this will help you get out of your league faster, and vice versa. League of Legends decides which team has a higher probability of winning in every match, depending on their Matchmaking Rating. If you win a match where the opponent team had been chosen as the more likely to win, your matchmaking Rating (and League points, potentially) will increase quite a lot.
The term "Elo hell" has existed since the very beginning of ranked games. In other words, Elo hell means that some players cannot rise up from a hopelessly low rating. For instance, let's imagine that in the first 10 ranked games the player encounters AFK or leavers in their team and he/she loses 6 games. Then this player loses one more game and is determined into Bronze with a low Matchmaking Rating. Because of being placed here, the player gets teammates with low gaming skills, leavers, or those who cannot bring victory to their team. The idea of Elo hell lies in the fact that players with a higher level of gaming can find themselves much lower than they really should be, and it could prove quite difficult for them to climb out of this pit due to the low quality of teammates offered to them.
Does Elo hell truly exist, or is this just a myth?
Players with poor ratings will tell you that Elo Hell does exist and they're stuck there. Players with high ratings and most of the community will tell you that it's a myth. And they will all be wrong.
It all depends on the amount of games you've played. Statistically, Matchmaking rating and the league system are well-qualified to estimate the community. In individual cases, players' ratings can get significantly lower due to factors that are out of their control. There's always the possibility of bad internet connection, feeders and poor teammates. So if you've played only 30 games, some bad luck can easily qualify you below your real league. On the other hand, if you've played 300 this will be enough to qualify you into the league you deserve despite a few mishaps and low-performance partners.
It should also be noted that bad luck can find not only you, but your opponents as well, with equal probability. So your personal skill and your overall understanding of the game starts to determine your overall success. If you're deciding whether or not to take part in ranked play, you need to answer this question: do you have enough time to play so many games that this will overlap any bad luck in the early matches or not? If no, then you probably shouldn't do this. If the answer is yes, however, then go for it!
I'd like to quote Day9, a player of Starcraft: "Your matchmaking rating and league position are not a measurement of your skill, it's a measurement of your progress in the ranked system." Imagine two players start playing their placement matches. One is a total newbie at LoL, while the other one has thousands of normal games behind him. The second player is much more skilled and well-prepared for his opponents. The fact that they both ended up in Silver does not mean that they have the same level of skill. There are many skilled players who are below their position, just like there are many players high above the position they should occupy.
This is particularly true in Silver and Bronze divisions, where the presence of good or bad luck in the placement games easily puts you into a division which does not correlate with your genuine skill. Rank only then depicts skill when the player has achieved an almost unchangeable win/loss ratio during hundreds of matches and is not working on improving himself as a player any more.