How competitive it is totally depends on how many other Philosophy students apply, there is a fixed place that the Philosophy department can fill, and no other department can have that space. If they don't find anybody who's suitable, then they won't send anybody.
I considered applying for the History department's exchange slot this year. You have to have a letter of parental support, be excellent academically and have the support of academic staff, prove that you can afford the stay and write a personal statement as far as I remember. Basically, they want to know that you can be independent because you're going to be a long way from home and all of your support networks (I know that sounds a bit corny, but it's true). In the end I decided not to apply, partially because my parents weren't too happy about it, but also because I was a bit worried about settling back into Durham again in my final year when I hadn't really found my feet at that point.