It comes from a Slavic word which meant something like "Border-land" or "At-the-edge-land". For a long time the area around Kiev was a border area of the Polish-Lithuanian Commonwealth, and the region around Kiev came to be known simply as "The Borderland", or ѹкраина (Ukraina).
According to Fasmer the word is first dropped in the 12th century Hypatian manuscript for "borderland", specifically for the area of Kiev Rus bordering Hungary. And since Kiev was sacked by the Mongols in 1240 most of what used to be the Kiev Rus and is now the Ukraine became the subject of numerous wars between Muscowy/Russia, Lithuania/Poland and the Tatars/Crimea which would only come to an end once both Poland and Crimea were annexed in the 18th century.
Still "Borderland" remained one of it's bynames akin to how "the Border" remained also a term specifically for the for border between England and Scotland for a long time after the Acts of Union.