こそ is a 副助詞（ふくじょし） (adverbial particle) in Japanese that primarily replaces either
を or が. Its main role is to highlight the preceding noun (or noun phrase) as being the the most important piece of information in relation to the rest of the sentence. In English, this is an effect that is primarily achieved through things like bold text, underlining, or emphasizing a particular word in speech. If we were to make a direct comparison to an English statement, then things like ‘precisely because it’s (A)’, or ‘rather it is due to (A)’, are quite similar to
こそ’s function.
こそ can be used directly after any noun that would usually take the
を, or が particles, so long as that particular piece of information needs to be emphasized.
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この曲（きょく）こそ俺（おれ）がずーっと探（さが）していた曲（きょく）だ！やっとタイトルが分（わ）かった。
This song is exactly the song I have been searching for! I finally figured out the title.
今度（こんど）こそ勝（か）つぞ！
I will win for sure next time!
The reason that こそ is able to replace が, but not は, is due to the fact that が primarily highlights specific pieces of information, while は nominates general topics. This means that they have completely opposite functions. To make things easier, the three particles can be thought of in the following way:
は- Weakly highlights specific information.
が- Strongly highlights specific information.
こそ- Very strongly highlights specific information.
こそ is often used after names or pronouns, as a way to reply to thanks/apologies. In these situations, it expresses that the speaker feels equally (or more) obliged to say what was just said to them by someone else.