No one knows the origin of the word diatonic. Its derivation is obscure. However, it has been defined since at least the middles ages as a scale of 7 tones. What makes a scale diatonic is the interval between each tone. These intervals are not the same throughout the scale and as consequence the black keys of a piano are grouped in 2s and 3s.

Here is how (taking the diatonic scale of C as an example): Going from the first tone of the scale, the next note up is a whole tone to D. The next tone up from this is also a whole tone up to E. However the interval between the third and fourth tones E to F is a semitone (half tone). The next three tones are F, G and A - they are all whole tones apart. Finally we get to the seventh tone B and its interval to the C above is a semitone (half tone). A diatonic scale has five whole tone intervals and two semitone intervals with the semitone intervals being spread as far a part as possible.