She was from a minor noble family that served the Tsars when they were ruling Poland; her father died in the 1830 uprising and she became a ward of the Tsar.
This is the heart of her story from her Wikipedia article: “...Julia served as lady-in-waiting to Tsesarevna Marie Alexandrovna, wife of the future Tsar Alexander II and sister of Prince Alexander of Hesse and by Rhine. She met Prince Alexander while performing her duties at court in St. Petersburg. The Tsar did not approve of any liaison between his son's brother-in-law and a parvenu, and so the two arranged to leave the St. Petersburg court. By the time Julia and Alexander were able to marry, she was six months pregnant with their first child, Marie. They were married on 28 October 1851 in Breslau in Prussian Silesia (present-day Wrocław, Republic of Poland).
Julia was considered to be of insufficient rank to have any of her children qualify for the succession to the throne of Hesse and by Rhine (Hesse-Darmstadt); hence the marriage was considered morganatic. Her husband's brother, Grand Duke Louis III of Hesse-Darmstadt, created her Countess of Battenberg in 1851, with the style of Illustrious Highness, and in 1858 elevated her to Princess of Battenberg with the style of Serene Highness. The children of Julia and Alexander were also elevated to Prince or Princess and addressed as Serene Highness. Thus, Battenberg became the name of a morganatic branch of the Grand Ducal Family of Hesse..."
She had five children: 1) Marie of Battenberg, 2) Louis of Battenberg who served the British navy and is father of Louis Montbatten of Burma who is stepfather to Prince Philip and Alice who is Prince Philip's mother, 3) Alexander, Prince of Bulgaria, 4) Henry of Battenberg who married Queen Victoria's youngest child Beatrice and became parents of Queen Victoria Eugenie of Spain (Ena), and 5) Francis Joseph. From her arise the present monarchs of Spain and the United Kingdom and the now deposed monarch of Greece.