The Imam’s role, as laid out by the Quran, can be summed as follows:
1) To possess the religious authority and source of emulation, and the juristic dimension of clarifying the religious concepts like doctrines, ethics and laws. From this follows that he should be the only one to be obeyed and followed, and therefore his words and actions are on par with the words and actions of the Holy Prophet (s). 
2) It is evident that this role requires the Imam to be infallible to the same extent as the Holy Prophet (s) was (i.e. any speech or action that goes against the position of servitude towards God). So the requirement of infallibility is for conveying the religious concepts, and not to prove his ability to lead the people and manage their affairs, as the Sunni school (mis)understood.
3) And once their infallibility is proven, the philosophy of selection/appointment becomes clear, since it (infallibility) is a hidden quality and cannot be established through election and choice of the people, but through divine selection and appointment.
4) The above points do not remove the fact that the divine scripture and narrations indeed have given the political leadership to the Imam as well. 
5) The continuity of Imamah will become clear when I address the existential dimension of the Imam in later posts.
So the framework for these posts should be clear with respect to the role of Imamah to consist:
1) The existential role (takweeni)
2) The juristic/religious role (tashree’i)
3) The political leadership
4) The best moral/ethical example
Also, the fundamental aspects of Imamah can be summarised to be:
+ Divine selection/appointment
+ Special knowledge acquired through non-conventional means
 See Surah Al-Hashr:7 – وَمَا آتَاكُمُ الرَّسُولُ فَخُذُوهُ وَمَا نَهَاكُمْ عَنْهُ فَانتَهُوا – ‘And whatever the Messenger has given you – take; and what he has forbidden you – refrain from.’
 See Al-Ma’idah:3, 55 & 67 –
الْيَوْمَ أَكْمَلْتُ لَكُمْ دِينَكُمْ وَأَتْمَمْتُ عَلَيْكُمْ نِعْمَتِي وَرَضِيتُ لَكُمُ الْإِسْلَامَ دِينًا – ‘This day I have perfected for you your religion and completed My favor upon you and have approved for you Islam as religion.’
إِنَّمَا وَلِيُّكُمُ اللَّـهُ وَرَسُولُهُ وَالَّذِينَ آمَنُوا الَّذِينَ يُقِيمُونَ الصَّلَاةَ وَيُؤْتُونَ الزَّكَاةَ وَهُمْ رَاكِعُونَ – ‘Only Allah is your Vali and His Apostle and those who believe, those who keep up prayers and pay the poor-rate while they bow.’
يَا أَيُّهَا الرَّسُولُ بَلِّغْ مَا أُنزِلَ إِلَيْكَ مِن رَّبِّكَ ۖ وَإِن لَّمْ تَفْعَلْ فَمَا بَلَّغْتَ رِسَالَتَهُ – ‘O Apostle! deliver what has been revealed to you from your Lord; and if you do it not, then you have not delivered His message’