The MDA framework is a way of looking at and understanding games through three main components. To help with the explanation, consider the following situation.
In the game Left 4 Dead 2, you are shooting through hordes of zombies with a team of yourself and three other people. There are special enemies which can "pin" down players, completely incapacitating them. They must be saved by their allies or they will die. These are the mechanics of the game. How the game works. This is built into the source code of the game, and is purely logic.
Because of these mechanics, the game is very teamwork oriented. Players try to stay together, because they know they need their team mates to keep from getting "pinned" down. The opposing team, playing as the special enemies, will often try to separate these players, to make them easier to pin down.
These are the dynamics of the game. These are not built into the code. There is no rule saying players must stay together, buy they chose to because of the mechanics.
This teamwork oriented gameplay then can give players a sense of comradery or fellowship. They may learn to rely on each other and work together effectively. This is the aesthetics. The emotions caused by the dynamics. This is obviously not written in the code, or even shown tangibly in the game. Yet it is a very important part of the game.
Players tend to experience these three aspects in the order I told them. They learn the mechanics first. Once they understand how the game works, they develop dynamics. Once they start using these dynamics, they will experience the aesthetics.
Developers have to work in the reverse order. The Aesthetics are the end goal, and the developers often have a aesthetic, or a theme in mind when they start. They then have to think of how to make the players feel these aesthetics; the dynamics. What causes a sense of fellowship? Teamwork! Staying together! Covering each other's backs! Then they must decide what mechanics would encourage these dynamics. What would keep players together? The threat of incapacition if they wander off!
Acosta, Keyvan, et al. "MDA: Mechanics, Dynamics, and Aesthetics." 100
Principles of Game Design. Ed. Wendy Despain. Illus. Raymond Yuen. San
Francisco: New Riders, 2013. 30-31. Print.
Hunicke, Robin, Marc LeBlanc, and Robert Zubek. "MDA: A Formal Approach to Game
Design and Game Research." CiteSeerX (2004): n. pag. Print.