Actually you can. You need to be rooted in order to access the internal system memory, which is where your apps and all system data are stored. The Incredible has a separate internal memory storage partition that is formatted as flash memory, just like a memory card, which is why you get 2 separate drives when you connect your phone via mass storage- 1 is the memory card, and one is the internal memory. From what I've found, you can't move files from the internal memory, but you can copy them to your memory card.
Using Astro:
/emmc is the internal memory. Now unless you decided to put files on the internal memory, the only thing you'll probably have on there are photos, unless you changed the option right away when you got the phone, because it defaults to internal memory as the storage location. (Photos are stored in /emmc/DCIM/100MEDIA). To copy any file to the memory card, long press on it, and choose Edit->Copy. Now back out and go the folder on your memory card where you want to copy the file and press the Edit button up top, followed by Paste.