Justice is a unisex name that really took off after 1980. It was pretty rare in the early 1900's and only given to boys. It wasn't until 1975 that the name was given to more than 5 girls in a year - 10, to be exact, and to 28 boys. After that the number of boys kept increasing, while it was still rarely used for girls. Something changed after 1985, when suddenly it increased from 5 girls, to 36 in 1992, and then even more suddenly it jumped up to 175 girls in 1993. Then there was a shift, when the number of girls rose even higher and outranked the boys for a couple of years, then it shifted back to being used for boys more, and it stayed that way until 2011. Now it ranks at #525 for boys and #452 for girls, as of 2015.
It's a virtue name, being one of the four cardinal virtues, but also a meaningful word-name, a title, and concept. Justice is English through Latin origin, meaning "administration of the law," and related to the name Justus. Use as a given name also started in honor of the French surname Justice. In ancient Rome, Lady Justice was the personification of the term. It is one of the oldest ideas to be considered, and one of the earliest people to having musings on the concept was Plato in ancient Greece. It often represents balance or diving consequence, and as a society we still deeply value justice today, even seeking careers to administer justice in the sense of the law.
Justice has also been the name of songs, TV shows, films from the early 1900's and early 2000's, a 1910 play, and animated characters. The real namesakes that may have encouraged popularity of the name include wrestlers Sid Justice and the female wrestler Justice, or the actress Victoria Justice who was born in 1993. A few celebrities have used it for their kids, including Ziggy Marley, Jensen Ackles, and John Mellancamp.
This name is banned in New Zealand for being a title, just like Duke or Princess (which are also banned.)