The meaning to thickness of line should in essence be obvious, it means what it says, how wide or narrow the line actually is has an impact on how our brain relates to that line in context of what is surrounding it and the tonal value of the line also has an impact on what is seen, when I say tonal value I am talking about how light or dark the line is in tone.
If you draw a circle with a wider, darker line along the bottom area it will look like it is the bottom of a sphere and will start to look like a ball shape rather than simply just looking like a circle. This also gives the bottom half of the circle or sphere more weight because the wider line is more substantial especially if it is also darker in tone it will attract the eye giving more emphasis and importance to it, this also creates the illusion of light and shadow that is often used to emphasize the under areas of shapes we draw suggesting the shape is three dimensional.
Please take a look at the drawings of the two circles 1 & 2 below to see an example of what I am trying to explain also take a look at 3 & 4 these lines and circles have been made with a 5 mm, a half cm flat pencil, notice how the line varies in width giving it the look of a twisted ribbon. Number 5 shows how lines can go from a hard definite edge to a more subtle less definite edge that can be used to great effect in your line drawings. These different types of line can be used to create light and shadow so as to suggest the illusion of form and shape but still maintaining the quality of being a line using this within your line drawing can start to bring your line drawings to life.
The dragon drawing below was created with pen and ink it puts very little emphasis on line quality, it is a line that is consistent in thickness giving little or no quality other than just being a line but even so it does create the image of a dragon through the use of drawing lines with nothing more.

