Will you briefly (within 5 sentences) tell me how the Magna Carta affected the U.S. C.J. system?

Answer 1

The Magna Carta was a major step towards "due process" and "rule of law".
Due process means that legal decisions are based upon facts presented by both sides before any decisions are made. People can not be penalized first and then have their case argued later. This has been developed to include the rights to jury trial, reasonable bail, and public defenders.
Rule of Law means that decisions are made using consistent rules that apply to all. We follow rules even if they are always in our favor and expect others to follow the rules even when they are not in their favor.

Answer 2

The main thing is that it guaranteed trial by jury--a jury of one's peers.