The English verb "vacate" comes from the Latin word vacātus, the past participple of vacāre, meaning "to be empty" or "to be free".  The word entered English in the 17th century, initially with the legal sense of making something void or null, and later developed the more common meaning of leaving or quitting a place or position.  In the 18th or 19th century the meaning shifted to "to leave or give up" a place or position, a sense possibly influenced by the related word "vacant".  

According to the Oxford English Dictionary (OED), the verb "vacate" was first used in English to mean "make legally void" or "annul," in the mid-1600s, with the earliest evidence found in the writing of William Prynne in 1643.  
The sense of "leave, quit, or give up" a place was recorded later, in 1791. 

Examples of "vacate" used in a sentence: 
"On Tuesday, he became the sixth head coach to vacate his post." 
"He should vacate the room not later than 12 o'clock noon." 
"They were required to vacate their offices and return all university property in their possession." 
"Hotel guests are requested to vacate their rooms by noon." 
"I sat down in the chair vacated by my mother. One of their tenants vacated without notice.

Examples of "vacate" using the legal sense in a sentence:  
"The judge decided to vacate the jury's verdict after new evidence came to light".  
"The homeowner filed a motion to vacate the foreclosure judgment, arguing there were irregularities in the legal process".  
"The council members were forced to vacate their seats on the committee after they were found to have violated ethical guidelines". 
"After a significant zoning change, a number of businesses were forced to vacate their buildings in the downtown area".