A resophonic or resonator guitar is different from a resonator banjo, where the name refers to the round wooden back to increase the sound volume. Inside the body of a resonator guitar is a special thin aluminium cone to get more volume out of the guitar.
The dobro is a type of resonator guitar and was designed in the 1930s by the Dopyera Brothers in USA - hence the name 'dobro'. The resonator cone is covered by a round metal plate with many cut-outs in 4 halfround patterns. The bridge rests on the cone via a spider-like construction. Above this big coverplate are two separate round soundholes, which are covered with small grills. Between those grills are 3 small open soundholes. The neck is square and the frets are only for orientation because the nut is heightened so that the strings are quite high off the fingerboard, to make it easy to play the dobro laying flat, with a steel. The tuning machines are turned around (to the front) to make tuning easier. Some dobros are made with a normal halfround guitar neck and a low nut, to be played like an ordinary guitar.
The name Dobro is generically associated with the single-inverted-cone resonator design, as opposed to the tricone and biscuit designs which are both similarly associated with the National brand.
The dobro is mainly used in bluegrass music.
The model shown is probably a Dobro Professional Model 85 from about 1930.