こそ

It is X that…
X is precisely…
Noun + こそ

こそ is a particle that adds emphasis to the thing preceding it.
Unlike も (Even, too), こそ emphasizes the specificness of a word. It’s kind of like a stronger version of が. 
こそ replaces を and usually は. It fills even after に and で. 
It may be used with が for even more emphasis.

こそ tends to be used for strong affirmative statements, and is commonly (not always) used to express something contrary or unexpected. 

Common Expressions

こちらこそ – No it is I/me/us/we who should….(be thankful, etc)

そちらこそ – No, it is you who… (Worked harder, etc)

これこそ – it is that that is…

今度こそ – This time we will

今こそ – It is now that…

Examples

• かれこそが王に一番ふさわしい
  It is He that is most fit to be king. 
  
  
• 簡単な作業こそ注意すべきだ。
  It is simple work that you should be the most careful with. (Easy to make mistakes).
  
  
• 今度こそうまくいく
  It is this time that it will go well. 
  
  
• 辛いときこそ頑張るべきだ。
  It is the tough times that you should try harder.
  
  
• 悲しい時こそ元気にふるまうべきだ
  It is when you are sad that you should act energetically.
   
• これこそ、私が求めたウエブサイトだ
  It is this, (this is it) the website I was seeking. 
  
  

Comparisons

• 彼が一番ふさわしい
  He’s the most suited.
  
  
• 彼こそが一番ふさわしい
  It is he that is the most suited.
  
  
• 勉強すべきだ
  You should study
  
  
• 勉強こそすべきだ
  It is studying that you should do.
  
  
• 彼が強い
  He is strong.
  
  
• 彼も強い
  He is also strong.
  
  
• 彼こそが強い
  It is Him that is strong (No one else is truly strong).