What is the meaning of tinyint(N)? When we use an argument length with numerical data types, as far as I know this specifies the display width.
I tried the following:  

mysql&gt; create table boolean_test (var1 boolean, var2 tinyint);    
Query OK, 0 rows affected (0.10 sec)   

mysql&gt; show create table boolean_test;   
+--------------+-------------------------   
| Table        | Create Table
+--------------+-------------------------  
| boolean_test | CREATE TABLE `boolean_test` (  
  `var1` tinyint(1) DEFAULT NULL,  
  `var2` tinyint(4) DEFAULT NULL  
) ENGINE=InnoDB DEFAULT CHARSET=latin1 |   
+--------------+---------------------------  
1 row in set (0.00 sec)  


First of all tinyint is a 1 byte value. So what is the meaning of tinyint(4)? There can not be 4 digits.  

mysql&gt; insert into boolean_test values(101,112);  
Query OK, 1 row affected (0.03 sec)   

mysql&gt; select * from boolean_test;  
+------+------+  
| var1 | var2 |  
+------+------+  
|   10 |  112 |  
|  101 |  112 |  
+------+------+  
2 rows in set (0.00 sec)  


I see that in tinyint I stored a 10 and 101 and I could get back these values despite that it is defined as tinyint(1).
Shouldn't I see a 1 for var1? I.e. just 1 display digits?
Data-wise, tinyint(1), tinyint(2), tinyint(3) etc. are all exactly the same. They are all in the range -128 to 127 for SIGNED or 0-255 for UNSIGNED. As other answers noted the number in parenthesis is merely a display width hint.

You might want to note, though, that application=wise things may look different. Here, tinyint(1) can take a special meaning. For example, the Connector/J (Java connector) treats tinyint(1) as a boolean value, and instead of returning a numerical result to the application, it converts values to true and false. this can be changed via the tinyInt1isBit=false connection parameter.