[Nexus 4 Q&A, Help & Troubleshooting] Rarscaryfrosty:
Graphics Designer/Photographer here. Depending on what rom you have (stock or custom), you may have different camera options, so I'm going to go off the stock settings in the Nexus 4 camera.

Flash:

I typically leave flash off, sometimes I have it on if I know it's a dark place (indoors, parties, bad lighting). A lot of the times, the flash can create a white-ish haze, or even blow out details in photos. Flash can also produce a lot of glare on reflective surfaces which can be annoying and ruin a photo. If I can shoot a photo without the flash, I'll do so and touch it up later to improve it. Although sometimes just because you don't need the flash doesn't mean you shouldn't use it. Camera have a setting called "ISO" (You can't change this on our phone). Typically in a bright sunny environment, the ISO will be lower, causing a less grainy image. In darker scenes, the ISO automatically kicks up higher and adds grain to the image to help hold details which would otherwise be lost due to the low lighting. (This is also noticeable on old film cameras depending on the ISO speed of film you purchase, 100 being lowest, 400 being typical, 800+ being high grain)

Exposure:

If an image is too dark, flash on, or flash off, you can always try to turn the exposure up by +1, or +2. Same for if an image is a bit too bright, you can turn the exposure down. I use this a bit less on cell phone cameras since it feels a bit more fake than what you'd find on a real camera. It can be helpful though in bright/dark scenes. Play with it yourself to get the hang of it.

White Balance:

This mainly modifies how color is perceived by the camera when a photo is taken. Color temperature (in kelvins) can change how white looks under different lighting. A piece of white paper may look pure white when outdoors in the bright sun, while inside your lamp makes it seem creme/yellowish. Adjust the white balance to the proper lighting condition will better allow you to get more accurate colors in your photos. If you have a florescent light, switch the setting to that. If you have incandescent lighting indoors when trying to snap a photo, switch to that. On this mode, you're better off leaving it on automatic most of the time, but if you have time to make changes based upon the lighting conditions, do it.

HDR:

I wouldn't use this mode if you're trying to capture high speed motion or anything moving. It's best for still shots you know you can capture. HDR quickly takes 2 photos split seconds apart from one another. It adjusts the settings of the camera to capture the most detail in the darkest portions of the scene, and the brightest portions of the scene. Then it combines the photos into one image creating a scene you normally would not have been able to shoot without HDR. For example if I'm outside in a sunny day and I'm shooting a photo of some trees, the camera is going to adjust itself to capture the most detail and color from the trees. Because the sun is so bright, normally the camera would just blow out the sky and make it pure white, or extremely bright. With HDR on, it'll shoot a photo metering the color and values of the trees, then shoot another metering the color and values of the sky, then stitch them into one nice photo.)

I hope I helped some. I'm trying not to use too much photography terminology which might confuse people who aren't too familiar with manual photography.