Appoggiaturas are accented non-chord notes which move by step (up or down) to a chord note to resolve.
In this example, the chord is C major. The note D is an appoggiatura. It does not belong to the chord, so it is a non-chord note. It falls on the beat (not between beats), so it is accented. It moves by step to the chord note C, which is its resolution.
In early music, appoggiaturas were normally written as small-sized notes, to make it clear that the notes are decorative and not part of the harmony. By the Classical era this practice was dying out, but the appoggiatura as a decorative figure was (and is) still widely used in its written-out form (in normal sized notes).
Appoggiaturas are mostly found in the melody part, or in a soprano line.
In this tune, which is in G major, the E, A and C are best described as appoggiaturas, each resolving downwards to a chord note. This allows the harmony to move along with one chord per bar. The only alternative would be to use a much larger number of chords, which would sound very hectic.
Appoggiaturas are often approached by a leap, as the E and C are in this example.