What do Oxbridge look for in a personal statement?

For Oxford and Cambridge, the focus will always be upon your relationship with the subject. The personal statement needs to explore what you love about it, why you love it, and what you have done inside and outside of the curriculum to persue this passion. Furthermore, you need to express an opinion - ideally one which highlights a particular facet of your subject which you are especially keen on. This is important because Oxbridge are looking at you as a prospective student first, and a person second. As such, they want to know how you think, how you engage with the subject matter, and whethey you can make an academic argument. These are the skills you need to be showing (not telling) in your statement.