A reaction mechanism is writing step by step how a chemical reaction works. Usually, only the overall change can be seen in a reaction. The things made in between react too quickly to be seen. These are called intermediates, and in going from one intermediate to another a transition state is crossed. However, it is important to understand all the steps that make the total change. This is because then one can understand more difficult reactions or try to make a reaction work in a certain way.
There are many type of reaction mechanisms. In organic chemistry, the more common ones are nucleophilic substitution, elimination and addition. People sometimes use arrow pushing to draw how electrons move around during a reaction. This makes it easy to see which bonds are formed and which are broken during the process.