DSLR is an acronym that stands for 'Digital Single Lens Reflex' and refers to a camera's optical design paradigm.
The 'Digital' in DSLR refers to the camera producing an image via a digital imaging sensor that turns light into a digital image. The DSLR is an evolution from SLR cameras that use light-sensitive film to produce images.
The 'Single Lens Reflex' part of the name refers to the physical inner workings of the camera. Light enters through a single lens that is attached to the front of the camera. The light exits the back of the lens and is re-directed to the camera's viewfinder via a series of mirrors and prisms. When the shutter button is pressed the mirror at the back of the lens quickly flips out of the way, letting the light hit the digital imaging sensor (or film in the case of an SLR)