HDRI is a process where you take pictures of the same view or scene with different exposer settings and then added together inside an image processing software like photoshop or photomatix. This process is used a lot in 3d now days because it recreates the same lighting as what you shot with your camera. They are now starting to use it a lot more in games because it give a much more realistic look and can be done because how technology is progressing so fast.
This is a HDRI picture of a city, you can see that there is more dynamic range. This is achieved by setting the exposers to different settings then putting them together in photoshop ect.
This is a panoramic HDRI picture this is what you when creating HDRI lighting inside a 3d software like Autodesk Maya.
These pictures below are some of my own tests of HDR pictures which i created with my canon 600d and photoshop.
This is my first ever HDRI i have created and feel that i can do a lot better by missing around with the settings in photoshops HDRI created. To get this type of image i set my camera to take 3 photos at different exposure settings. The i imported them into photoshop merge to HDR Pro, what is adobes own HDRI software built inside photoshop. Once photoshop has combined the images together you can play around with the settings like shadow, detail, highlights and many more.

This picture is a quick HDRI panoramic i have done inside photoshop, this is the type of this you need to do for visual effects. The other way is to get a chrome sphere and take three shots with different exposures, this way is a lot easier to create HDRI panoramic than the way i did. it.
Here are some screenshots of the process i did to create HDR images inside photshop. There are special HDR softwares out there but i find photoshop to do a pretty good job.
This screenshot shows you how to bring pictures into photoshop and merge them together to make a HDR image.
This window shows you how to search or the image files you want to merge together. You can selected as many as you want and it will to the rest of the work for you.
Here i am just searching for my own images i would like to merge together.
Once you have selected all of your images the next step is to press ok and let photoshop work its magic.
Once photoshop has finished processing this window will come up and it will have different parameters you can mess around with to get the look you are looking for. Once you have finished the next step is to press ok and it will turn what you have created into one image file.