On the guitar we can play a chord progression and the melody line at the same time.
The melody is usually played in the upper register ie. the top strings, and the rest of the chord is played to fill out (harmonize) the melody.
We can also play the bass line on the bottom strings in the same way . We can therefore have three parts playing simultaneously - the melody line, the bass line, and the chords in the mid range to fill it out.
This can involve some advanced finger technique, which is attainable through constant practice and exercise. A fingerstyle picking technique is required rather than straight strumming.
For an example of what can be achieved, take a look at the following arrangement of 'Yesterday' by the Beatles. Just about any song can be dealt with this way on a guitar.