Seeing 
The stability of the atmosphere determines how much fine detail you can spot at high power with a telescope.
If the atmosphere is very calm, and detail is very crisp (the stars do not appear to twinkle, even at the horizon), the seeing is rated 10. This is extremely rare.
If the atmosphere is extremely turbulent, and lunar and planetary detail are fuzzy even with your lowest magnifications, the seeing is considered to be Zero.
Typically, it ranges between 2 and 7. This rating is rather subjective, based on your own personal observing experience. As you get more practice, your ratings will be fine-tuned.
Transparency 
Transparency is based on the magnitude of the faintest star naked-eye visible overhead.
It is rated from 1 (very hazy--with only a few 1st magnitude stars visible) to 6 (thousands of stars visible with the Milky Way quite obvious).
Light pollution plays a big role in the transparency around cities...it is rarely better than 2 or 3.
This is why dark sky observing sites are so important.