That's the magic of "cześć". But seriously, as far as I am concerned, any particular explanation cannot be given here. It's just a universal word and we use it both for greeting and when leaving. If you cannot accept using "cześć" twice - you could say "na razie", "do zobaczenia" or "trzymaj się" for a farewell. The equivalent of "cześć" at the beginning of a meeting, would be "witam". Regarding the word etymology, please take a look here: http://en.wiktionary.org/wiki/cze%C5%9B%C4%87

Yupp, you can say "oddajmy CZEŚĆ kapitanowi" which means "let's give honours to the captain. The roots of "Cześć" used as a greeting, come from the word honour.

Oh! Now I know!!! This word is connected with the word 'honor' in Polish, 'honour' in English and 'честь' in Russia! So it means something like 'честь имею' = 'this is an honour' !! :) Quba, thank you for the link! It helped me with etymology :)