As with regular computers, files deleted from a phone may not be lost forever. This is good news if you've ever accidentally deleted data. Of course, the first line of defense against losing data is to keep a backup -- locally and remotely. If you were caught without a backup, however, there are some things you can do to get that data back.
The first thing to do is stop using the device. Files aren't immediately "deleted" the second you hit the delete button. Instead, that space is just freed up to be written over with new data. The less you use the device after deleting data, the better the chance is to recover it that data.
Next, you can try plugging the Android device into a Mac or PC. The phone will give you an option to connect as a camera, Media Transfer Protocol (MTP) or simply USB Mass Storage. You'll want to connect it as a storage device, because then it will appear like any other drive and you'll be able to browse through the folders on it. Once the phone is connected as a drive, you can run recovery software like Recuva to unerase the files.
For more on how to recover lost files on an Android device, check out this article at instructables.com.