Explaination
well personally i always describe C/D as "C slash D", you always describe the chord first then the change in bass note. sometimes people refer to it as C over D but you just have to get used to it being called both ways or the many variations i guess.
anyway heres my two cents worth: you will see some common chords like C/B, D/F#, G/F#, A/C#.
usually the common ones are based on this principle: inversions of four part or more voicings of a chord. to make it simple take Cmaj7, Cmaj7 is made up of three notes: C E G B, arranged from root to the 7th voicing. now if we were to invert it meaning put C as the top note instead you would get : E G B C. its not a different chord (well lets assume that for now) but now instead of C in the bass you have E in the bass so we call it C/E. because we inverted the bass note, its known as the first inversion.
and to cut it short, if we take the other preceding notes then we make different bass notes for the Cmaj7 chord. so therefore C/B would be the Cmaj7 chord in its third inversion.
thats the simple part of the common "slash chords".
the other ones like C/D or G/A could either be :
1)extended chords like D11 or A11 but notated differently.
2)other chords that because the voicings above the varying bassnote forms a triad is named so.
3)or just because to put a non-diatonic bass note over a triad just makes it sound cool