The most important idea from the Magna Carta that influences governments today is the idea that the executive (the king back then, presidents and prime ministers today) does not have unlimited power. Magna Carta made the king share power with his barons -- today executives must generally share power with legislatures.
Another important idea is the right of habeas corpus, which means that a person may not be held in prison unless there is some legal reason for holding them.
Finally, there is also the idea of due process. This is the idea that a person can not be punished (have life, property, or liberty taken away from them by the government) unless they have been legally convicted of a crime.
Together, all of these mean that the we can see the influence of Magna Carta in limitations on the powers of modern governments.
Though the original purpose of Magna Carta in 1215 was only to protect the interests of the feudal class, later it became an instrument for securing better justice for the common people.
For example, the charter made it obligatory for the king to seek the advice and consent of the barons in all important matters. It also ruled out raising of special taxes without the consent of the barons. Later provisions of this type in Magna Carta led to methods of government in which no law could be made or tax raised without the consent of institutions such as parliament representing interests of people.
Perhaps the biggest contribution of Magna Carta to the establishment of the modern governments was sowing the seed of the idea Government by rule of law, documented and accepted by people, which replaced the the earlier concept king having some kind of Divine right to impose his will as law.