Here is my understanding of how the ranking system works. Wins cause you to gain both LP and increase your MMR. Typically the game with try to match you with players that have a similar MMR as you, however it will also take into account how often you are winning those matches. Consistently winning or getting big win streaks will cause the system to recognize that you are better then the current competition, causing you to start gaining more LP for each win and raising your MMR. On the flip side if you are struggling to win games you will start to lose more LP and your MMR will decrease. Basically the system is trying to see what tier you belong in, if you are winning it will try to move you up, and if you are losing it will try to move you down.
The reason you can be matched up with people that appear to be ranked higher then you is caused by two things. If you are doing well at your current tier the game will start trying to match you up against better competition to see if you need to move up. The other possibility is that the opponent has been performing poorly and is losing MMR but has not yet lost enough LP to drop from their current rank. This would cause them to be matched up against someone of similar MMR or someone who is performing very well and taking on higher competition.
Hope that helps and explains how it works..