Answer by Balaji Viswanathan:
A President role is fundamentally to add respect to the rule of the people. While the Prime Ministers can be colorful and demagogic, a President has to be above politics. He/She is the upholder of the Constitution and the idea was to bring a highly respectable figure who will be looked up by all sides. When a scholar like Kalam heads the state, India walks high in pride among world nations. People feel happy about being in a democracy. Of course, the real power will be vested in people who can do the "dirty job" of running the government [saints cannot run a nation].
Think of figures like Kalam, Radhakrishnan (happy birthday to you) or even KR Narayanan. They would not have been elected to any high post with power. The post of a President is for such figures, who are very respectable and whose judgment should be respected by those in power.
A President for instance, can veto a bill passed by the Parliament. The Parliament can overrule the veto by passing the bill again, but the judgment of such an eminent person will be listened to in most cases and will get the attention of the people. If the Parliament is overruling a President's veto, then something is wrong. If people believe in the respectability of the President, then the Parliament is toasted come next elections. This sort of keeps the Parliament from going off the rails making highly unfair bills.
Our Constitution's elaborate process for electing a President in theory should bring better candidates, but our voter's excessive reliance of the Congress party has made this Constitutional guarantee weak. President Fakhruddin Ali Ahmed, for instance, didn't do anything to impede Indira's imposition of emergency. A strong President could have posed more hurdles for her.
Presidents often help bridge between different groups in a nation and between India & rest of the world. Kalam and Radhakrishnan did their role well. The role also lets the democracy bring minorities and other communities who would not easily get elected to the top in a majority rule. A third of the Presidents were Muslim, for instance. This helps create role models and also keeps communal tensions low.