Man idk why people downvoted you for asking questions.
MMR stands for match made rating. Essentially it's a number that ranks you in the total population of your server. This number is used to determine who you play with and against, their MMR number will be close to yours.
The amount of LP you gain or lose depends on the difference between your team's average MMR and the enemy team's average MMR. If your team's is higher, you'll gain less LP and lose more since the game knows you're more likely to win. If your team's MMR is lower, you'll win more LP and lose less since the game knows it's a tough game.
There are no reliable sites to check your MMR. I think the best we have is op.gg which will show you a rough estimate of your MMR and let you know how you stack up to averages at your rank. Generally if your MMR is above average you'll climb, and you'll drop if it's lower than average.
This is a summary, some of it may not be perfectly accurate. RIOT has not disclosed exactly how MMR works in LOL.