A Stuffed shirt. What does it mean?

It means, someone who is very formal, pompous, or old-fashioned.
who behaves in a very formal and old-fashioned way and thinks that they are very important. 
     You can refer to someone as being a ‘stuffed shirt’, when you are suggesting is that the individual is rather old fashioned in his outlook. 
The expression also used that the person in question is a pompous individual. 
we can use this to suggest the kind of person who believes that his ideas are extremely important. 
        If you call a man a stuffed shirt, you mean that he is formal and boring. 

To call someone a "stuffed shirt" is of course, derogatory. 
The shirt is given more credit than the person wearing 
(or stuffing) it by the person wielding this insult. 
It is used widely in describing politicians or a loud-mouthed.

synonyms: blimp, bloated aristocrat, pompous ass, pompous person, twit, a pompous, self-satisfied, and inflexible person 

How to use.?  
Person who is perceived as useless, stupid, or given more credit than he/she deserves. You can use stuffed-shirt before a noun. 

Some sentences to understand this idiom

1.  I have little patience with the dress rules of stuffed-shirt establishments.
2.  I had heard he was a bit of a stuffed shirt.
3. This office is full of stuffed shirts; there’s no one fun that I can have a laugh with.
4. “He is no less than a stuffed man,” suggesting that this person was so full of himself that he was, in fact, quite empty.
5. Bhagavan was a true intellectual stuffed shirt.
6. Shalini clearly felt no empathy towards the stuffed shirt towering above his wife.
7. That new student is a stuffed shirt.
8. That lecturer is a stuffed shirt.
9. He's nothing but a stuffed shirt.
10. Our CM is just a real stuffed shirt.
11. Mr. shivakumar considers himself to be a stuffed shirt.
12. He is a stuffed shirt type of professor.
13. My boss is a stuffed shirt.
14. He only seems like a stuffed shirt when you first meet him.
15. Since Dr. sudhakar seems to be a stuffed shirt, I try to avoid him.
16. Krishna isn't stuffed shirt like Bhagavan -- he's a friendly, informal guy like us ordinary people.
17. In a pinstriped suit he instantly looked like a stuffed shirt.
18. The club members are not just a bunch of stuffed shirts.

so guys, dont be stuffed shirts, get some stuffs in your mind. Be intellectual.