According to the Quran, a Muslim is one who has absolutely surrendered to Allah and his commands and believes in pure Tawhid (the oneness of God) that isn't tainted with any Shirk (polytheism) and this is why the Almighty has introduced Prophet Abraham (pbuh) as a true Muslim in the Quran.
Definition of the term "Muslim" according to the Quran.
According to the Quran, a Muslim is one who has absolutely surrendered to Allah and his commands and believes in pure Tawhid (the oneness of God) that isn't tainted with any Shirk (polytheism) and this is why the Almighty has introduced Prophet Abraham (pbuh) as a true Muslim in the Quran.
According to the Quran the true religion is Islam (surrender) as Allah says in the Quran:
Indeed the only true religion in the sight of Allah is Islam.[1]
Therefore all of those who embraced the holy religion of their time are called Muslims by the Quran, meaning that Jews and Christians were Muslims until they had to change to the new religion which was Islam, because they had surrendered to Allah.
It is obvious that today the term Muslim is used only for those who embrace the religion of Prophet Mohammad (pbuh), because they have shown their surrender to Allah through believing in Islam and obeying his commands. According to this definition today people of other religions are not considered Muslims because they have actually rejected surrendering to Allah through turning away from the new religion (Islam) that was sent down for them and they are no longer considered Muslims.
It must be noted that a true Muslim is one who not only believes in Islam but actually practices it in his life. So not only Muslims should submit to the one God and believe in the prophets but they should also act according to Islam's social teachings like respecting other people's rights in society and its teachings that relate to one's personal life like fasting and praying.
Notes:
[1] إِنَّ الدِّينَ عِندَ اللَّـهِ الْإِسْلَامُ. (3:19)