Monarchy makes its first appearance in the vedic period. Scholars are still debading whether monarchy existed in Indus. We cannot be sure unless the script of Indus is deciphered one day. So, leaving the happenings of Indus aside, the first appearance of kings in India is in the vedic period. The concept of monarchy was a natural extension of leadership. IN ancient lands, man lived in groups. Each group had a group leader. When groups collided, the leaders played a vital role in victory or defeat. During the vedic and post vedic periods, these groups became more and more bigger. They fought with other tribes (referred to as daasas in vedas), they fought internally. The battle of 10 kings is vividly recorded in Rig veda. So kings emerged out of group leadership. Vedas called the king "Raajan" or "Raajanya". God Indra was their supreme deity - the warrior god who could bestow victories.
Kings were considered to be reflections or even avatars of lord vishnu. When you hear Lord Vishnu has Bhoomi devi and Sri devi all it means is that the King (who is Lord vishnu) owns land (Bhoomi) and Money/ riches (Sri). This was the initial personification. Later on this original concept was lost and bhoomi and sri were worshipped as independent godesses.
This is why even thiruvalangadu copper plates say rajaraja had sankha and charkra regais. It means an attempt to show some reflections of lord vishnu in king's physical features.
Thus, kings came into existance in the second millenium.
Perhaps the most interesting development of all in the evolution of monarchy is that people felt that the powers of king should be kept under check.