Sayoonara
This phrase literally means, "In that case...", and is basically a "goodbye".
Its construction breaks down into two parts.
Because sayoo is a dated word, conversations that end with sayoonara are usually ones that have been very formal and official. This is why some people will feel that saying sayoonara is childish--almost no conversation will have the same old world feel as was present in the samurai and shogun days, and it doesn't match the mood of the present day. That being said, everyone will still understand what you mean.

Sayoonara incorporates the long o sound, and is written alternately in romaji as sayounara, and has entered the English vocabulary as "sayonara". This is due to some interesting quirks in transliterating Japanese to English, and by no means makes any of these spellings incorrect.