Slash-Chord. On the left side of the slash you have a chord, on the right side the lowest tone (bass). The C/Bb (say „C over Bb”) is a C major chord with a low Bb played in the bass.
The C major chord consists of the tones C (1), E (3) and G (5). The bass on the right of the slash can indeed, but does not necessarily be part of the chord on the left. In this particular case the bass is not directly a part of the C major chord, but at least it adds a minor 7th to it. It's one of those special cases where it sometimes make sense to write it as C7/Bb. You'll find C/Bb and C7/Bb with about the same frequency.
Example chord progressions: BbC/BbDb/BbEb/F
Here different major chords are played over one static bass note („pedal bass”). The notation C/Bb of course makes much more sense here than C7/Bb.
CCmaj7 C7/Bb …
In this case the notation C7/Bb helps to recognize that the major 7th (maj7) is descending to a minor 7th (7). When playing a guitar solo that for sure can accelerate the decisions which scales, arpeggios or guide tones to play.
Here another chord progression: CC7/BbF/AAb
Ok, one more... CC7/BbA7 Dm7 Fm6 C