When MAME4droid is first run, it will create a folder structure for you on the internal memory of your Android device.
The default folder is: /sdcard/MAME4droid/
This folder contains all the other folders MAME uses as well as some basic configuration files.
Since MAME4droid does not come with game ROM files, you will need to copy them to the /sdcard/MAME4droid/roms folder yourself. These should be properly named, ZIPped MAME v1.39u1 ROMs files with the filenames in all lower case.
MAME4droid (0.l39u1) version 1.7 (January 7th, 2015) made some changes to the default locations and installation due to the enhanced SD Card security of KitKat and Lollipop versions of the Android operating system. This can have an adverse effect on previous installations of MAME4droid users while helping those with these versions of Android.
Your ROMs are still safe and sound – right where you left them which is probably on your external microSD card. The quick fix is to simply go into Options->Settings->General->Change ROMs Path. Point this to your actual ROMs folder (not your MAME4droid folder). If you have no custom filters or have 'favorites' turned on, you should now see all your ROMs as you remember them.
Even changing your ROMs path, you may appear to lose configuration settings like favorites and more. One fix? Copy all the files (not folders) from the root of your MAME4droid folder (mame4droid.cfg, favorites.ini, etc) to //sdcard/MAME4droid. Overwrite any files already there. Restart MAME4droid.
If you are an advanced user, you may relocate the entire installation (not just the ROMs folder) to another location (like the one you had before). You'll need the full path to your installation. You may change this under Options->Settings->Advanced->Installation Path. Be careful using this option; if you chose a valid but incorrect path, a complete new installation of MAME4droid will be made there. Recommended for experienced users only.
MAME4droid can make use of many advanced MAME features such as bezel and marquee artwork and sound samples (for games that require them). Place appropriate assets into the respective folders. Check out the Resources and Assets section for asset resources.
artwork/ -> Artwork directory
cfg/ -> MAME configuration files directory
hi/ -> Hiscores directory
nvram/ -> NVRAM files directory
roms/ -> ROMs directory
samples/ -> Samples directory
snap/ -> Screen snapshots directory
sta/ -> Save states directory