To produce such an image takes the coordination of numerous modern technologies. I'll give you a quick basic rundown. It begins by using magnetic resonance imaging (MRI) which in itself is dependent on the concept of nuclear magnetic resonance (NMR). NMR in simplest terms uses a giant magnet to align the atoms within a sample, here a brain, and then maintaining that alignment. They then pulse the sample with electromagnetic radiation (light) and the atoms shift from their alignment slightly. Different atoms that are bound to different things will then return to their alignments at different rates and with different resonances. They use these differences to create an image when doing MRI.
That in itself is pretty awesome and generates great images, but what DTI does is exploit the fact that water molecules inside the human body do not act completely randomly. In fact the water molecules within the glial cells and myelinated axons diffuse (random spreading out of stuff) much differently because they are bound within a different environment. So a super-duper computer looks at water molecules with NMR and basically computers the vectors associated with their motions to generate a DTI image.
DTI provides a unique way of visualizing these brain components noninvasively for applications such as locating lesions or tumors as well as providing a new research technique for neural degrading disease such as Alzheimer's or multiple sclerosis.