That means go to the beginning of the text you want to copy, so from the first letter of the sentence, to the last letter.
Let's say you wanted to copy this sentence:
Arnie ate too many cookies.
You'd click at the 'A' and keep the mouse button held down, and drag it to the end where the little period (.) is. In Internet Explorer (probably your web browser) this will not copy, you need to RIGHT click the text and click on 'copy' from the menu. In mIRC however, as soon as you highlight text and let go, it copies the text. You can then press CTRL+V to paste it.
It seems that was more of a sidenote for copying, your question seemed to relate to the TAB nick completor function that zaz described above. As another example of it, if you type 'Me' in a channel that I'm in, and then press the TAB key, it will complete to 'Mentality' automatically. (Note: Not with the colours, that was just to make it clear).
Regards,