Other good file manager apps include ES File Explorer, Astro File Manager, and Total Commander (all free).
The way that Android sets up directories can be confusing, especially when it comes to internal memory and the external SD card. For example, if your phone was advertised as coming with 16 GB of memory (not counting any SD card), about 6 GB are usually taken up by the system and about 2 GB are reserved for app storage. The remaining 8 GB is referred to as "Internal Storage" or "Media Storage," and can be used to store files like photos, music, and videos. Apps can also be moved from App Storage to Internal Storage if you're running low on the former. This Internal Storage is usually designated by the directory "/mnt/sdcard," even though it isn't physically an SD card.
If you have a physical microSD card inserted, it comes up under the directory "/mnt/sdcard-ext." The main purpose of external SD cards is storage of media files, because you can't move apps to external SD memory, only to the Internal Storage. Some 3rd party apps may give you the option to save data to the external SD card.
The stock camera app gives the option of saving photos or videos to internal or external storage (look under the Settings menu of the camera). If internal, the directory is "/mnt/sdcard/dcim/camera"; if external, the directory is "/mnt/sdcard-ext/dcim/camera."
Hope that helps!