The T-Mount adapter is a circular bracket attaches to a digital camera body via the standard lens socket. The other end accepts the screw thread of the focuser or a Barlow lens. This allows you to use your DSLR camera in "prime focus" mode.
Pictured below is a Canon EOS T-Mount adapter, although they are available for pretty much any SLR make.
The T is said to stand for Tamron, a Japanese manufacturer that released the first of a line of aftermarket camera lenses to fit 35mm SLR cameras. As a common mechanical interface, the T-mount allows components of various manufacturers to be interchanged and assembled. The T-mount is a solely mechanical specification. Electrical or mechanical connections, such as for autofocus, are generally not provided.