My most favorite part of being an application analyst is the opportunity to own something. Being an application analyst directly impacts the company you work for because the work that company does on your application(s) entirely depend on you doing a great job. My measure of how I am doing is how much I accomplish without taking up other IT resources, including DBA, programming, and contract management.
The challenge that comes with this is to collaborate well. Naturally collaboration means some groups will not get everything they want when it conflicts with another group. Coming from a service background I dislike saying no, but it is a very important part of smart application progression.
The biggest advice I would have for a new person to being an application analyst would be to be happy when the big ugly project is looming. You will never accomplish as much as you do during the big, ugly, conflict filled projects. Swing for the fences and understand that is is OK to make mistakes running full speed. A systematic development process allows for this and for iterations to both correct and continually improve.