Can someone explain to me how this function works in relation to a GUI output.

Public Overrides Function ToString() As String

My program do some calculation and conversions and displays the resluts in a list box. I need use this function but i am not sure how it affects my output.

ToString() gives the textual respresentation of the object. This means with numbers that, for example, number 3 gets displayd as string "3".
ToString() also accepts format string as a parameter and this gives the full power of it. For example -123.ToString("X") returns hexadecimal representation of the number (=FFFFFF85).
You can read more about string formsts from the MSDN documentation.
Since it's overridable method you can have your own implementation of it in your own class.