1. Some technologies used in space flight are under severe sanctions from other developed nations, to slow down the development of missile technology of lesser developed nations (developed in the context of military technology). There is a lot of impetus to research and develop those technologies in-house. This leads to a huge gain to India in terms of technical skill, research infrastructure, research know-how, experience, etc. This leads to "down-the-hill" technological advantages in related fields (for ex. medical, industry, etc.). Since the research is public domain, related technological improvements are available for cheap. (A recent example is the opening up of Li-Ion battery technology by ISRO for interested parties in the Industry)
2. Launching a rocket, especially a manned one, is only the tip of the iceberg. There is a huge amount of work that goes into making that happen, a lot of which is Research & Development. Rocket technology directly leads to better and advanced missile technology. This ensures (though some may argue otherwise) a credible deterrent to enemies, ensuring longer periods of peace. This directly improves lives of the citizens.
3. There are numerous examples of technology developed to enable space flight trickling down to medical and industrial uses.
In fact, the same can be seen in Formula 1 races. Many technologies we take for granted in modern mass market vehicles (ABS immediately comes to mind, several safety features, crumple zones, etc) are the result of extensive developments in F1 racing scenes.
Even in management, having two teams competing with each other to solve a particular problem, almost always leads to an explosion of ideas and generally a better final solution to the problem at hand. Case in point is in the development of the iPhone, etc.