Earth, Mars and other planets orbit the sun in elliptical, roughly egg-shaped orbits. The transfer orbit puts Mangalyaan into another, roughly egg-shaped orbit around the sun. That transfer orbit has to be calculated to intersect the Martian "egg" at exactly the right place and time to rendezvous with the planet. The gravity assist, using Earth's field to impart velocity (velocity refers to speed in a specific direction), is designed to conserve fuel rather than get to Mars quickly. A minor error could mean that Mars is missed by millions of kilometres. Slingshots are difficult to calculate and each transfer orbit presents its own challenges. That Isro got it right in the first shot is a major achievement.
The chosen transfer orbit involves four course-correction rocket firings over the next 10 months. Each of those will be increasingly delicate. As distance from Earth increases, real-time telemetering becomes impossible and the course corrections will have to be pre-programmed with contingency measures built in to perform autonomously. If all goes well, the fourth stage will be almost totally autonomous, with the vessel firing its rockets to force itself into Mars orbit. Again, this manoeuvre will be calculated to minimise fuel expenditure. Even with minimal fuel consumption, it takes a 350-tonne rocket to deliver a 1,350-kilogram orbiter with a 13-kg scientific payload. Prior to Sunday, only the National Aeronautics and Space Administration (Nasa), the Russians and the European Space Agency had succeeded in demonstrating slingshots. The completion of the third and fourth stages will mean facing up to even more complex challenges. On their track record so far, it appears that the boffins at the Satish Dhawan Space Centre will be up to the task.