Many scholars, such as Shaykhul Islaam Ibn Taymiyyah رحمه الله and Imaam Ibn Khaldoon رحمه الله, state that humans are social creatures. It is clear from the Qur'aan that every human being is part of a greater society and it not an island unto himself. Allaah سبحانه و تعالى says in the Qur'aan,
In general, from birth, a human is a person's son or daughter, another's brother or sister and yet another's nephew or cousin. Furthermore, almost everyone has neighbours and many have spouses. The guidance of the Qur'aan produces not only the Islamic individual with respect to his worship and character, but beyond that it also guides humans in their relationships to one another such that they create a society based on mutual understanding, rights and responsibilities all according to the guidance of the Creator, the All-Wise, the All-Knowing. This society works together as a whole and uses all of its resources in ways that are pleasing to Allaah سبحانه و تعالى.
Allaah سبحانه و تعالى has made it clear that one of the purposes for which He revealed the Qur'aan is so that it may be the law of the land and used to judge what is right and what is wrong. Allaah سبحانه و تعالى says,
This society will be unique, based on the clear guidance from Allaah سبحانه و تعالى. It will have its own principles and values that it will do its best to propagate and uphold. It will be something distinct from the way of ignorance (jaahiliyyah) or non-Godly societies that this world has seen and is witnessing. Allaah سبحانه و تعالى indicates that there is only His true and perfect guidance or there is the way of ignorance and the way of desires of mankind. Note this implication in the following two verses of the Qur'aan,
The sole raison d'etre of such a society will be to worship Allaah سبحانه و تعالى and serve His cause. It will stand for truth and justice in every realm of life and throughout the world. For example, within the society itself, Allaah سبحانه و تعالى tells the believers that they do not have the right to allow others to do evil or spread evil in their midst. 
Allaah سبحانه و تعالى says in the Qur'aan,
(Soorah Aali 'Imraan, 3:110)
This is one essential aspect of this Islamic society guided by the teachings of the Qur'aan: its members work together to eradicate evil and promote good. They not only purify themselves but they do their best to purify everyone in their society as a whole.
But this proper Islamic society which the Qur'aan can guide humans to not only spreads good and eradicates evil from within but it also feels the responsibility of spreading the word of Allaah and the true submission to the One and only God to the rest of the world. This can be seen in the Quranic injunctions concerning, for example, Jihaad. For instance, Allaah سبحانه و تعالى says,
Hence, when a person reads the Qur'aan, he must realise that the Qur'aan is showing him or guiding him to his rights and responsibilities towards all of mankind. When the person reads the Qur'aan in this light and attains this guidance from the Qur'aan, his behaviour and actions will change such that he becomes beneficial and helpful for his own society and the world as a whole: calling people to the way of Allaah سبحانه و تعالى and helping to establish the Quranic commands in this world.