What exactly ist the new swipe gesture to move the cursor?

It's explained in the iPhone manual:

http://www.textasticapp.com/iphone/manual/lessons/How_can_I_move_the_cursor_using_swipe_gestures.html

Does that mean that this function is an iPhone only function? I was not able to reproduce it on my iPad.

I saw this new function in the iPad update text.

No, I added the same feature to the iPad version. It's just not in the iPad manual yet, that's why I pointed you to the iPhone manual.

Make sure you have the latest version (4.2.1) installed.

Just swipe quickly (!) to the left or right side. This will move the cursor one character at a time. If you use two fingers, the cursor will move a word. If you use three fingers, the cursor will jump to the beginning or end of the line.