Strictly speaking the appoggiatura as an analytical term refers to an accented dissonance that is approached by leap and left by step. However, as discussed below, the importance of this embellishment in the Classical style means that, in practice, many accented dissonances that resolve by step are referred as appoggiaturas even if they are not approached by leap.
The appoggiatura is the most marked dissonant embellishment in tonal music because it is approached by leap, unlike the accented and unaccented passing notes, which are approached by leap and the suspension, which is prepared.
The third of the above examples below shows a double appoggiatura - two notes are initially dissonant with the chord being embellished and then both resolve by step. The very common type of double appoggiatura is the cadential six-four, which is sometimes analyzed as Ic.
The term appoggiatura is often used to refer to an ornament that is particularly common in the Classical era, in whicha note on a strong beat is decorated by a 'leaning' note that resolves onto it by step. When written as an ornament the appoggiatura is shown as a small note slurred to the note it decorates as in the example below (note that the acciaccatura has an oblique line through the stem and flag and is performed by being 'crushed in' just before the note it decorates):
When this sort of 'leaning' dissonance is written out in music from the classical era, it is often referred to as an appoggiatura whether or not it is approached by leap. In the example below, three appoggiaturas resolve by step onto a C major chord: