Translation:This glass is full, and that one is empty.
As a linguist (but not a native Russian speaker, though I have been studying/speaking it on and off for 30 years), I'd be inclined to agree with Sam, with one small exception: the пол- does not come directly from половина, but is apparently a prefix in and of itself, meaning "half." The word половина derives from this original prefix пол- or полу-, and we see it in many other common word forms as well, e.g.: полгода, полчаса, полдень, полтора ('one and one half,' which comes from this prefix пол- + второй, so it could literally be translated as "half two.") In fact, these prefixes пол- and полу-, which can also be translated as "semi," can be combined with many other nouns to form a new word meaning "a half a [noun]" or "semi-[noun]" (the latter seems to be more common with the prefix полу-).
I don't usually like to cite Wiktionary as a source, but (1) I have found it to be usually quite trustworthy, (2) it often gives etymologies, and (3) there is a very good list of useful examples under the listing for полy-:
It comes from половина, or to be more precise, from the prefix пол-, which means "half" (see my comment above). The word половина, which is understandably more commonly known to Russian students than the prefix itself, seems to have been creatеd from this prefix пол- + -овина, the latter being a suffix used to create a noun from an adjective, prefix, or other noun.
Although they would seem to be related due to the similarity in spelling and pronunciation, the two words derive from different Proto-Slavic roots: polъ for пол- and pьlnъ for полный, although there could be a connection further back. This proto-Slavic root *polъ "half" does, however, explain the presence of the same prefix in Czech, Polish, Ukrainian, and many other Slavic languages, as they are all descended from Proto-Slavic.