Tonguing is separating a note from the one in front of it by momentarily stopping the air flow through the whistle with your tongue. You stop the air flow by very briefly and lightly saying "tuh" into the whistle at the beginning of the note.

Slurring is the absence of tonguing, so you keep a steady stream of air flowing through the whistle as move your fingers to the next note; in classical music terms this is called playing legato. Traditional Irish music uses less tonguing that other genres of music.