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Yandere (ヤンデレ) is a portmanteau of two Japanese words yanderu (病んでる), meaning to be sick, and deredere (デレデレ), which is defined as strongly and deeply exhausted, infatuated, moonstruck, head over heels, or lovestruck, but in this case used for "lovestruck." -from google

There are several definitions which can be found online, however I am going to paraphrase all of them and say that it refers to the emotional development of a character who becomes romantically attached to his/ her love interest in a way which some describe as psychotic.
It is a state where he/she exhibits her love in an exaggerated form (examples from wikipedia: kidnapping crushes, poisoning food that is to be eaten by a romantic rival, or forcing the romantic love interest to commit a double suicide (shinjuu 心中)).
It is basically someone who would do extreme things due to his/ her lovesickness.

Thank you ^^ I really couldn't follow what others ware saying in the comments I was reading because I didn't know the meaning of this word.