Sections
Kibou (希望): what it means in anime
希望
きぼう · kibou · hope; wish; aspiration JLPT N3
Kibou means "hope" as a noun: 希望がある ("there is hope"), 希望を捨てるな ("don't give up hope"). It also means a wish or request on a form.
Where you hear it 2 of 42 series
Lines from the Japanese subtitles of episodes 1–3 of each show. A translation is shown only when it clearly matches the line; counts are subtitle lines containing the word.
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K-On! · 8 lines in episodes 1–3 · this one from episode 1
みんな 入部希望者が来たぞ
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Polar Bear Café · 5 lines in episodes 1–3 · this one from episode 1
条件に希望はありますか？
Usage and nuance
In dramatic anime 希望 is the counterweight to 絶望 (zetsubou, despair), and the pair is a cliché of its own. Danganronpa built an entire franchise on 希望 versus 絶望.
The everyday sense is milder: 希望する means to request, and 第一希望 is your first choice on an application. K-On and Polar Bear Cafe use it that way, which is why it appears in gentle shows too.
The warmer, more personal verb is 願う (negau, to wish), and 望み (nozomi) is a hope or wish in plain language.
Hear 希望 in K-On!8 lines in episodes 1–3 · tappable subtitles · free, no account