An eidetic memory, is by definition, a memory than retains completely and totally all information possible by touch, smell, sight, hearing, and taste. Someone with an eidetic memory will be able to recall with complete and total clarity all of these senses. Not only that, but the ability to do so will be stored in ones memory upon coming in contact with any of these senses for perfect and total recall. Photographic memory is another type of this memory, but mainly specialized in the visual category, however both allow for perfect recall.
A common test to determine if someone has a memory of either of these categories is to place an image, such as a painting or picture they have never seen before. The test administrator then removes the picture or image, and asks the test taker to describe certain details of the image. A person with an eidetic memory will describe the picture or image as if it were still in front of them, like the test taker never even removed it.
Anyone can have a memory of this capability. Generally, just about everyone has a few memories that they can think back to and “see” and “feel” the event again as if they were back wherever the event occurred. This is even more prevalent with traumatic or incredibly emotional memories, where the person can recall exactly how they felt, what they saw, heard, smelled, even the taste of the event. Everyone has this capability, though only a few can use it to their advantage naturally without any training or brain optimization.
For those of you that are not lucky enough to have such an ability naturally, there are a few things you can do to obtain such an ability. Braintropic.com has a guide on how you can obtain an eidetic memory with tons of simple changes and a really great (although a bit pricey) training program to use in conjunction with those simples changes. It also has a bunch of other stuff meant to enhance your brain and help you utilize your studies to their max. I recommend checking out their nootropic stacks, or the sleep hack guide.