A diminished fourth is an interval of four semitones.
The interval between C and E, for example, is a diminished fourth as it contains four semitones.
In a lot of common scales, such as the standard major scale and the natural minor scale, the interval between the root on the scale and the fourth note on the scale is contains five semitones. This more common interval is called a perfect fourth. The diminished fourth is "diminished" as it is one semitone smaller than the more common perfect fourth. The diminished fourth is a "fourth" if it occurs between the first and the fourth note on a scale (or more generally between two notes with two notes in between).
In principle, a diminished fourth is the same as a major third. Both intervals contain four semitones. A diminished fourth through would refer to the interval between the root on a scale and the fourth note on the scale (or more generally between two notes with two notes in between) whereas a major third would refer to the interval between the root on a scale and the third note on the scale (or more generally between two notes with one note in between).
Even though the diminished fourth is not as common as the perfect fourth, there are scales that use this interval. An example of the fourth mode of the minor gypsy scale is D#, E, F, G, A, B, C and the interval between D# and G is equal to four semitones.
See also:
Intervals on the chromatic scale, Intervals on the chromatic scale (index)
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