HDR is a term that gets thrown around a lot these days although it seems a lot of people don't quite understand what HDR actually means. So basically HDR stands for High Dynamic Range and is a way of dealing with situations where there is a high dynamic range. Now effectively that means is the difference between the darkest and the lightest parts of the image. The human eye has a much better ability to see a variety of dark and bright areas with high detail at the same time. However, cameras don't have this same ability so you often find that you either have a photo where the bright areas are correctly exposed and the dark areas are really dark or you have the dark areas are visible but the bright areas have blown out cos they're too bright.
To combat situations where there is a bit difference between the brightest and darkest parts of the image, the camera will take a variety of exposures at different exposure levels. Typically it's three exposure but can be more. One photo is underexposed to give detail in the highlights, one is correctly exposed and the last is overexposed to give details in the shadow areas. You can then combine these three images to get an image that has all sections correctly exposed. To take the photos, you can typically use the exposure bracketing function of your camera which is will take three consecutive photos using the different exposure levels.
The process of combining the photos can be done in camera but is typically done on the computer. There is a dedicated software such as Photomatix but I personally use Lightroom CC's inbuilt HDR tool. HDR can also be achieved by a powerful technique known as luminance blending which is done in Photoshop and has the biggest amount of control over the final image. Be careful with HDR as it can be very easy to go into an over-processed look which is not appealing at all. Like with all processing, it looks best when it's not obvious what you actually did.
18mm 6s F7.1 ISO 100 - North Bondi, Sydney, Australia
18mm 6s/13s/30s F10 ISO 100 - North Bondi, Sydney, Australia
These two images were taken from North Bondi looking back towards the beach. This photo was taken at sunset and presents some challenging lighting. As such can see, we have a sky that's fairly bright and a foreground that is quite dark. For the first image I tried taking a balanced exposure and then boosting shadows and dimming highlights in Lightroom but this had limited success. So this left the option of using HDR.
The second image is a HDR blend of exposures. There are three separate images blended together in Photomatix. One photo was one stop underexposed, the second was correctly exposed and the third was one stop overexposed approximately. This is where you can get the camera to do the exposures itself using exposure bracketing where you are using a -1.0 - +1.0 EV.
The following image is an example of a HDR done using luminance blending. You can look up more about luminance blending online and Jimmy McIntyre writes a lot about how to use this technique.
10mm 0.5s/1s/10s F8 ISO 100 - Bronte Beach, Sydney, Australia
So HDR can be a very powerful technique to use when you have tricky lighting situations. Just be careful not to overdo it as it can make things look awful. Try to use exposure bracketing on your camera to make your life a lot easier. So next time you're out in high contrast scenes, try to use HDR to combat these issues.