Thanks for the Enwired's answer. This bugged me for some time.
To further elaborate Enwired's answer, it is the number of m's that the JTextField can display on the screen (panel or window).
Observations
new JTextField("mmm", 3); // this 3 is number of 'm' that we allow to fit in, please note that 'mmm' and 'abc' widths are different even though they are same character count, that is 3
For the above code it will display a JTextField with 3 m's width. (we can type more m's on this JTextField, but on the TextField it shows only 3m's)

If we type "abc" on this, there is still remaining space on the text field where we can accommodate another character like shown below,

new JTextField("mmm", 3);
so, the conclusion seems to be it (argument value 3) is not the number of characters that we can fit into JTextField, but the number of 'm' that we can fit in.