The core principle of Magna Carta 1215 is that no person is above the law, including the king. This was as radical a statement as it is fundamental to the cornerstone of the American Judicial System today. The Magna Carta forced the king of England to accept several new principles of government, among them, the right to be judged by a jury of ones' peers, the right to a speedy trial, and the right to be protected from an unjust punishment imposed by a government. The essence of the Magna Carta is that is gives political power to the otherwise powerless populous. This shift of power will serve as the catalyst towards 'innocent until proven guilty in a court of law (not the court of the king) by a jury of your peers (not the jury of the king) The English Bill of Rights 1689 and later the United States Bill of Rights 1791 are guarantees of civil liberties (freedoms), each having a common heritage...Magna Carta 1215.
I would say that the main impact of the Magna Carta on today's laws is in the idea of individual "due process" rights that is enshrined in that document. These rights continue to form the basis of the legal systems in countries whose law is descended from that of England.
For example, the rights to trial by a jury of one's peers and to be free from punishment except if one is convicted in a trial are in the Magna Carta. These are really the cornerstones of our legal system in the US. We form our legal system around the idea that people cannot be punished without getting their "day in court."
These rights and others became the basis for the British legal system and that ended up influencing many other legal systems, including our own. In that way, the Magna Carta continues to have an impact today.