This Notation is for the Chord of C with a G Bass. Simply play a C Maj Chord, (the notes C E and G shown in blue), and then play a G note shown in red, played with the left hand.
The C/G type chords ( and similar others ) are very popular and bring a richness to the music with the bass note. Usually a bass not reflects the root of the chord, i.e. C Bass played with the Chord of C.