A crush is a slang word for a person for which one feels affection. It can be a verb, such as "He is crushing on his neighbor", or a noun, such as "That artist is my crush" or "I have a crush on that artist".
History.
The word comes from English slang, in which "crush" means a strong infatuation or crush, usually non-reciprocal. 
According to the Oxford English Dictionary, "crush" appeared as a noun appeared in the 14th century and referred to "a noise of violent percussion," such as rumbling or crashing, a noise element that was lost to the verb "crash". By the early 1600s, "crush" meant "a violent compression or pressure that knocks down, breaks, injures, or destroys." As a verb, "crush" can mean to compress or squeeze with force. In "The New York Times", one early use was in 1906 when a boy was reported as not crying when a train "crushed his toes". The emotional use of the word, in which one is "crushed" by anxiety or other negative emotions, developed simultaneously. Thomas Moffett wrote in 1599 "the hart-breake crush of melancholies wheele.”
The first recorded use of "crush" in a romantic sense is commonly considered 1884 in the journal of Isabella Maud Rittenhouse: "Wintie is weeping because her crush is gone". 
By 1895, "crush" referred to infatuation itself, as used by John Seymour Wood in "Yale yarns": "Miss Palfrey ... consented to wear his bunch of blue violets. It was a 'crush,' you see, on both sides". Eric Partridge has proposed that "crush" emerged as a variant of "mash", which was used in phrases such as "on the mash" and "make a mash with someone" to refer to flirting, as well as "masher" to mean a cunning, flirtatious man. "Crush" was reportedly used as a verb by 1913. The song "I've Got a Crush on You", with lyrics by Ira Gershwin, debuted on Broadway in 1928.
According to a study by the Zen content platform, "crash" is one of the most popular slang words among Russians aged 14 to 25, with 63% of respondents using it in their communication.