These are great questions, and the answers can vary by veterinary school. In general, all schools will want you to show that you have had exposure and experience in the field of veterinary medicine—this (hopefully) ensures that you aren’t surprised by the vet school and its content. Also, grades are important—this will show that you are able to handle the fast paced, large workload that is vet school. Letters of recommendation are key, these will come from those around you (hopefully at least one from a veterinarian you have worked with) who can comment on your attitude, abilities to work with others, your scholarly achievements, your work ethic, your problem solving skills, your abilities to handle stress and pressure, and who you are as a person in general. Being outstanding in these areas will help you to stand out, so give it your very best!
Before getting into vet school, I volunteered at a veterinary clinic. I started with cleaning cages, which of course is not a glorious job. But, my mother told me to do the best that I could with any task, so if my task was to clean cages, well then I would be the best cage cleaner that the clinic had ever had. This attitude led to me being offered a part time job, and then led to me being a veterinary assistant for them. The veterinarians that I worked with at this practice wrote me letters of recommendation that got me into vet school, for externships in the zoo field, and I am still friends with them today (as their colleague).