The C/E chord is a so called slash chord. On the left side of the slash you have a chord, on the right side just the lowest tone (bass). This chord is pronounced „C over E”.
The C/E consists of the following tones: C (1), E (3) and G (5)
The bass E is part of the chord here. That doesn't always have to be the case in a slash chord!
This major chord with a major 3rd in the bass is probably the most common slash chord at all. There's almost no pop or rock ballad, where you can't find it. In most cases you'll find it where the bass is ascending or descending diatonically (in half or whole steps).
Example chord progressions: Fmaj7 C/EDm7 respectively Dm7 C/EFmaj7 CC/EFG
For those who already know the diatonic chords of a major scale: the major chord with its major 3rd in the bass often replaces the chords on the IIIrd or VIIth scale degree of the major scale.
Therefore the C/E chord often replaces the minor chord on the IIIrd scale degree of the C major scale or the chord on the VIIth degree of the F major scale.
Diatonic chords of C major: CDm Em FGAm Bdim* Em and Bdim replaced with slash chords: CDm C/EFGAm G/B
Diatonic chords of F major: FGm Am BbCBm Edim* Am and Edim replaced with slash chords: FGm F/ABbCDm C/E
*) as 4-note chord (7th chord) not dim7. It's m7b5 then!!!