Just wonder, what means have number M at the field declaration like
field_name INT(M) ?

I have used to use it as length in bytes, mannual claim, that , but simple tests doesn't show any difference between int(1), int(3), int(5), int(11).

So basically, what does that number mean?

Gee it's like you found all the mysql forums today. ;-)
See this item

I think that the M digit, is only used for the ZEROFILL parameter, so if you do not use the zerofill, you should only use INT or INT(11) wich is the default.

NB: You better validate this info, I'm not sure about it.

CREATE TABLE testTable (
`a` INT(11),
`b` INT(11) ZEROFILL
);
INSERT INTO testTable (`a`, `b`) VALUES (1, 1);
SELECT * FROM testTable;

With this Query you should see the difference

thank you guys for the your help, all is clear for me now

INT(11) is not the default INT is. Any GUI that automatically assigns a length value to numeric data types is doing so incorrectly and really gives people the wrong idea about what values can be held in the data type.

but if I specify INT as a datatype in mySql, and then I export the table, it will export my INT field as INT(11)...

As you rightly quoted from the MySQL manual :
This means that any integer number that displays BELOW this width (as example: 4) will be padded with spaces (or if zerofill specified 0's) ,
will actually be producing :
note in column `a` you have 3,2,1,0,0 spaces in front of your number