A good answer to this question can really help you sell yourself in a job interview. Try this sample answer:
You are looking for someone that can easily fit into the department and seamlessly take on the responsibilities left vacant by the past employee. I not only have the experiences necessary to succeed in the position, including working with X, Y, and Z, I also fit in well with your department’s vision and have the ability to work quickly and efficiently to keep projects up to task. Other candidates may have some impressive qualifications of their own, but no other candidate is going to fit in as effectively as I will.
There is a lot of confidence in this answer, you rehashed some of your better qualities, and you stated specific reasons that make you a better candidate. You do not want to brag, but you certainly do not want to be humble, as you are trying to give the employer reasons to believe that you truly are the best candidate for the job.