A diminished 7th chord consists of four notes built one on top of the other. It is built up using intervals of a minor 3rd - a minor 3rd describes two notes which are 4 semitones apart e.g. C-Eb. The interval between the lower and top note is an interval of a diminished 7th, giving the chord its name. This chord is most often used when modulating to distant keys.
This is a diminished 7th chord built on C. Try it for yourself and hear how it sounds.
A clip showing how a diminished 7th chord can be used to modulate into different keys.