Photographers call it the golden hour or the magic hour. It's that time when the sun is near the horizon, or just below, and the character of the natural/available light changes. The light quality is best when the sun is 6-7 degrees above the horizon, and the effect ends when the sun is 6-7 degrees below the horizon. It's not always a fixed time, because it depends on the season and the distance you are from the equator.
Photographers and cinematographers often seek out the golden hour; it can add a striking tone to your photographs.
Now, the iPhone comes to the rescue. I've recently been using 2 apps that calculate the golden hour based on your location. One of the apps is pretty simple. The other actually shows you where the sun will be as it races toward the horizon, with a live camera view so you will know when it will be in just the position you want.
First off, let's take a look at Sun Scout. At US $9.99, it's not inexpensive, but it also does the most. Sun Scout uses the compass and motion sensors in the phone to superimpose the predicted position of the sun over a live view. I find I'm using it all the time so I know exactly where the sun will be to prepare a landscape shoot. The positions I got from the app for the sun were accurate, but you want to make sure to be clear of large amounts of metal or the iPhone's compass can get confused. I noticed that problem when I was standing too close to my car.
The other worthwhile app is Magic Hour. This free app is a bit simpler, but very useful. It tells you when magic hour is for your location, how long until it begins, and it can even send you a notification that it's about to start. You won't get sun positions, but you will learn the best time to take your pictures. Using the app is simple enough, and I found the calculations to be accurate.
Of course you may not be taking the pictures on your iPhone, but perhaps on your DSLR or pocket camera. No matter what you use, when you make an effort to take your pictures when the lighting is at its best, you'll be amply rewarded with images you want to keep for their sheer beauty. It's a great time to shoot landscapes, but it's also nice for taking pictures of people too.
I've included some screen shots from both programs in the gallery below.