With Android phones, you have the option of "moving" an app from the main application memory to the internal phone storage memory. This can help preserve your main application memory and allow you to install more apps, since the total application memory you have is probably around 3 GB (that's how much my original Razr Maxx has, anyway). The reason I put "moving" in quotes is that you're not moving the entire app to internal memory--you're moving most of it there, but some key parts stay in main application memory.
Now this is where it gets complicated. Android phones have several different storage areas:
1. Main application memory: As mentioned above, this is the 3 GB or so that the system uses to install apps. If you've used up all 3 GB, you can't install any more apps, which is why there is the option to move apps to ...
2. Internal phone storage: This is part of the onboard memory that came with your phone (i.e., not including your external SD card). If you have the 32 GB Maxx HD, it means there are 32 GB of onboard memory, but only 26 GB is available to the user (according to the Amazon Wireless site; the 6 other GB are used for the system and preinstalled apps that you can't get rid of unless you root the phone). Of those 26 GB of memory, around 3 GB are partitioned as main application memory as mentioned above, so ultimately around 23 GB are available on internal phone storage. This is where apps can be moved to if you choose that option.
To make things nice and confusing, if you use a file explorer app, you'll see that the directory for the internal phone storage is "/mnt/sdcard/," because the system regards it as an SD card. However, this is the only place you can move apps--you can't move them to the external SD card.
3. External SD card: This is the SD card you physically insert. You can't move apps here in stock Android (although I think an app like App2SD might allow you to, depending on the phone). The best use for the external SD card is for media storage (music, videos, audiobooks, etc.). Some apps (like the camera) can be set to save files directly to the external SD card as well.
The directory for the external SD card is "/mnt/sdcard-ext/". Simple, right?
I'm not sure why your phone is prompting you to move apps to the SD card. Do you have App2SD or a similar app installed?
The one caveat here is that I'm describing all of this from my experience with the original Razr Maxx on ICS. I'm not sure if anything has changed with Jellybean.