If you've ever strummed a guitar you will be aware of the 3 chord trick - I, IV, V.
These 3 chords can be used to accompany a huge amount of folk, pop and rock music. The V (dominant) chord is usually played in its 7th form ('cos it sounds good), so in your example of C major, those chords would be C, F, G7. The dominant 7th is that V7 chord arpeggiated.
Now you might ask OK why am I playing these "chords" on the violin? You will find as you look at music in more detail and begin to apply some simple analysis, that these chord progressions do occur quite regularly even in simple "one line" tunes. You will also discover (shock horror) diminished 7ths cropping up in the same way. It is the use of these devices that "implies" the underlying harmony of a piece even if it is only a single line being played with no chordal accompaniment. Lots of solo string and wind pieces are built this way.
It is when you can recognise the various common scale and arpeggio figures in a piece that sight reading becomes easier (so I am told
). You then read the sentence rather than each individual word or letter.
Right that's enough thinking for this time in the morning. I'm off.