I wrote my personal statement kind of like a narrative of my experiences and how that shaped my decision to apply to vet school. I was sort of a non-tradtional student, and I used the statement to explain certain aspectes of my application that would not be explained with just the VMCAS application. I used the space to tie in all my academic and work experiences and showed how they all related to the goal of becoming a veterinarian. It wasn't easy, but I think it was convincing enough.
Things to definitely avoid would be "I love animals", "I've always wanted to be a vet since I was three years old", "I love science and animals"-type statements. They are trite and cliche. You need to use this statement as a way of personalizing your application. There are thousands of qualified applications that come into schools, that are separated only by miniscule GPA points and animal-related experiences. The personal statement is your opportunity to show the adcomms exactly what you have to offer to them and what you have to offer to vet medicine.
I think it's also important to keep the statement brief (1000 words I think is ideal.) Good luck
Joanne