It's pretty simple when you think about it:

Store - Is what holds all the data your application uses.
Reducer - is what manipulates that data when it recieves an action.
Action - is what tells reducer to manipulate the store data, it carries the name and (not required) some data.

Reducer is usually in a format of a switch statement, 
that switches between all possible Actions (Cases) and 
then manipulates the Store data based on action. 
When a reducer data changes within the redux, the properties in your components are changed and then the re-render ocurrs.