Think Aloud is a qualitative method to evaluate the usability of a product or an interactive system (or a service). The tester is asked to conduct some tasks and comment everything he thinks or does outloud. Depending on what he is testing you can record his voice (for example during a website testing), film or follow him.
It's easy to conduct, doesn't require a lot of tools and can give really unexpected feedback, you just need sometimes to remind your tester to constantly explain his thoughts.
The good point of this method is that you will get an insight of what happens in the user's mind and any misconception of your concept will pop up quickly. You'll probably understand better his behaviours and decisions. On the bad side, people might not tell everything they think, to not disappoint or hurt you like it can happen when doing interviews.
One more important thing about Think Aloud but Testing in general is that you should compare results of tests conducted at the same time of the day. Depending on what you test, the user's tiredness, hunger... could influence his effectivness.
In Web design, the think aloud method can be really efficient combined with screen recording, eye tracking and face recording. Using these techniques will help you quickly see if the users understand well the navigation, find the buttons, the essential information, what attracts their attention, if they are disturbed by some interactions or if anything frustrates them.
I've conducted tests for the website Usertesting.com that records your voice and your screen while you conduct the tasks. At the end on the test, you need to answer some questions. If you think about testing your website or app, I would recommend you to register and conduct 1-2 tests as a user to see how other companies do it, the best way to learn!
You can use all these methods all along your process: with prototypes, digital mockups, a beta version or after the product has been released before improving it.