Why does Dropbox ask for my OS X administrator password?

Dropbox needs an administrator password for two reasons:

The first reason is to allow us to run the dbfsevents daemon when Dropbox is started. This is a tiny process that gets file system change notifications from OS X so Dropbox knows when files have changed. If you don't enter your password, Dropbox is forced to use a different OS X API (called FSEvents). This method is much more resource intensive (both in CPU and RAM) and isn't as reliable at detecting file changes in some circumstances.

The second reason Dropbox needs an admin password is to allow us to integrate into the Finder when Dropbox is started. This integration is required for icon overlays and the context menu to work properly.