Lexical Definition of Imamate
Imamate means leadership and Imam is attributed to someone –either righteous or vicious– whose conduct and ideas are followed by the people. The leader of the pious and the leader of the evildoer are both called Imam. Both meanings are mentioned in the Holy Quran too.
The Holy Quran states,
وَجَعَلْنا مِنْهُمْ أَئِمَّةً يَهْدُونَ بِأَمْرِنا لَمّا صَبَرُوا وَكانُوا بِآياتِنا يُوقِنُونَ
“And We appointed, from among them, leaders, giving guidance under Our command, so long as they persevered with patience and continued to have faith in Our Signs.”
وَجَعَلْناهُمْ أَئِمَّةً يَدْعُونَ إِلَى النّارِ وَيَوْمَ القِيامِةِ لا يُنْصَرُونَ
“And we made them (but) leaders inviting to the Fire; and on the Day of Judgment no help shall they find.”
 Surah Al-Sajdah (320: 24.
 Surah Al- Qasas (28): 41.