An augmented second is an interval of three semitones.
The interval between C and D#, for example, is an augmented second as it contains three 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 second note on the scale is either one semitone or two semitones. These more common intervals are called a minor second and a major second respectively. The augmented second is ”augmented” as it is one semitone larger than the larger of the two more common intervals (the major second). The augmented second is a “second” if it occurs between the first and the second note on a scale (or more generally between two adjacent notes).
In principle, an augmented second is the same as a minor third. Both intervals contain three semitones. An augmented second through 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) whereas a minor 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 that have a note in between).
Even though the augmented second is not as common as the minor and the major second, there are scales that use this interval. The harmonic minor scale in A, for example, is A, B, C, D, E, F, G# and the interval between F and G# is equal to three semitones.
Intervals on the chromatic scale, Intervals on the chromatic scale (index)