A diatonic scale is not a specific scale, but rather a way a scale (or a chord for that matter) is constructed and in that manner diatonic scales are the opposite to chromatic scales. Music that uses tones from a certain scale can be called diatonic, which is true about most music.
The term is going back to the antic Greeks there musicians separated octaves into intervals with names that all begun on dia-.
A diatonic scale is built on the intervals made by natural notes (i.e. neither flat nor sharp) and based on seven whole steps of perfect fifths: C - G - D - A - E - B - F. In modern Western music a scale is referred to as diatonic if it is based on five of these whole steps together with two half steps.
The Major Scale has this formula: Whole, Whole, Half, Whole, Whole, Whole, Half. The same is true for the formula of the Natural Minor: Whole, Half, Whole, Whole, Half, Whole, Whole.
Many scales are therefore diatonic including major, minor (the Harmonic minor is an exception) and modal scales.
Examples of non-diatonic scale are pentatonic, octatonic and whole-tone scales. Also in more obscured cases, like the Acoustic scale.
For this article Music and Twentieth-Century Tonality: Harmonic Progression Based on Modality and the Interval Cycles (Routledge Studies in Music Theory) by Paolo Susann and Elliott Antokoletz and Wikipedia.org has been used as a source.