A diminished third is an interval of two semitones.
The interval between C and D, for example, is a diminished third as it contains two 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 third note on the scale is either three semitones or four semitones. These more common intervals are called a minor third and a major third respectively. The diminished third is "diminished" as it is one semitone smaller than the smaller of the two more common intervals (the minor third). The diminished third is a "third" if it occurs between the first and the third note on a scale (or more generally between two notes with one note in between).
In principle, a diminished third is the same as a major second. Both intervals contain two semitones. A diminished third through 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 a note in between) whereas a major second would refer to the interval between the root on a scale and the second note on the scale (or more generally between two adjacent notes).
Even though the diminished third is not as common as the minor and the major third, 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 F is equal to two semitones.