There are at least two ways to answer this question.
First, we can say that the Code of Justinian was significant for the Byzantine Empire. The creation of the Code ensured that the Byzantine Empire would have a coherent set of laws that could be easily understood. The Code came into use around the year 530 and continued to be used as the basis of Byzantine law until the fall of the empire in 1453. Thus, the Code was significant simply because it was the basis of law for an empire for more than 900 years.
Second, we can say that the Code is significant to Western Europe as well. The Code never applied to this region because Western Europe was not part of the Byzantine Empire. Even so, the Code had a major effect in the West. It was written in Latin so it was easy for scholars in the West to use it. In the 11th century, scholars in Italy started to study the code. Before long, the Code was used to create a system of canon law. It was then used as the basis for secular legal codes. It eventually became the foundation of legal codes across all of Europe.
Justinian I, the Byzantine emperor from 527 to 565, sponsored committees of jurists who reviewed existing laws and, after eliminating outdated or contradictory laws, placed the laws and legal opinion into one work. The work was significant in that it formed the basis of western law for centuries and inspired the categories used in the Napoleonic Code of 1804, which was drawn up under Napoleon and abolished feudal laws.
Justinian's Code also placed regulations on Jews in the Byzantine Empire and began to take away the Jews' ability to practice what was formerly a legal religion. The code allowed the state to intervene in religious Jewish questions, and Justinian often did so. For example, he disallowed the reading of the Pentateuch in Hebrew. The code also prohibited Jews from giving testimony in court against Christians, though they were eventually allowed to testify in cases between Christians and the state. Though Jews had an elevated status compared to other non-Christians, they were relegated to a lesser status than Christians in the Byzantine Empire, and the law became an instrument in their oppression.