ぜひ
 

Hi, I would like to know what exactly does ぜひ mean? And how is the usage like?

okay. when you recommend something to someone, ぜひ means you should/you better example: ぜひあの映画を見てください。　You better watch that movie.

in another case, ぜひ can be the word to show that you're agree with someone's offer. example: dude A: "hey why don't we go drink this weekend?" you: " ぜひ "　( most definately )

Here are 185 examples using ぜひ: “ぜひ”の検索結果（185 件）：英辞郎 on the WEB：スペースアルク

If you're at all familiar with Chinese, the kanji way of writing it (not used in Japanese) is 是非. The first means "to be" and the second means "not." It doesn't make any sense to me, and it might even be 当て字. But I remember that I knew both from Chinese, and I was searching my Japanese dictionary for new words to learn comprised entirely of Chinese kanji I already knew, and I learned about 是非!

Thanks for the help, tipsygypsy and KyleGoetz.