There are situations, where basic shapes do not provide the flexibility you need to achieve a certain effect. Drop shadows, to provide a popular example, cannot be created reasonably with a combination of gradients. Filters are SVG's mechanism to create sophisticated effects.
A basic example is to add a blur effect to SVG content. While basic blurs can be achieved with the help of gradients, the blur filter is needed to do anything beyond.
You will get a full reference on SVG Filter effects on W3C Recommendation.