Weirdly, my dictionary (a lovely old Chambers that my mum and dad gave me in 1989) defines catharsis as purgative medicine having the power of cleansing the bowels – they missed that bit out in my drama degree. It does go on to say that it can also mean the purging of the effects of a pent-up emotion by bringing it to the surface of consciousness through drama — much more Aristotelian.
In classical terms, catharsis is the central experience, the raison d’etre, of fiction. People read partly as an escape from their own world, but also in order to see it reflected back at them through the lens of the hero or heroine’s heightened experience, so that they gain insight and understanding, but also a gratifying release of the tension you will have generated in your well crafted plot!
You can achieve this by putting your hero under incredible pressure so that they are obliged to change in order to meet the challenges you set them. There must be a lot to lose, and also a lot to gain. It’s very gratifying to feel wrung out at the end of a book – just as physical exercise gets the endorphins flowing, so a good book should give your reader a great emotional workout – that’s what you should be trying to achieve.