Integration testing is the process of testing interfaces among different module to see, whether they work as per requirement when they are combined.
Unit testing is done before Integration testing.
Real life example:
Lets manufacture a laptop. Here we can design and build Hard disk, Mother board, Dvd reader, lcd(or nowadays led) screen, web cam, keyboards etc. separately. After these parts are ready and unit testing is done, we will combine two or more parts and test, whether integrating these parts will work as per requirement or it produces some error. This is called integration testing. Generally it has two approach 'Top-Down' and 'Bottom-Up'. Sometimes 'Big-Bang' approach is also done where we combine all the module at one time and then integrate.Once the integration testing is done we do system testing and then Acceptance testing.