Classical is used to describe an established form of playing on the guitar that enables the performer to play the melody, harmony and bass line on the one instrument, very much like the piano, keyboard or harp.
Beginners should not be disheartened by this information because I always start teaching with single note melodies. (See FREE LESSONS).

By learning in the classical style, the pupil will not only play classical music (which can span over hundreds of years) but they will also be able to play folk, hymns, carols, blues, rag, jazz, pop etc.. However, it does take time and plenty of practice.

Other Names Used
The classical guitar can also be called "acoustic" as the sound is amplified  from the soundbox and not from any electrical device. Any guitar (steel or nylon strung) that does not need electricity to amplify the sound would be called an acoustic guitar.

The classical guitar can also be called "Spanish guitar". This is based on the traditional development of the guitar and not because the guitar is only made in Spain or that only Spanish music is played on it.

Flamenco is a style of Spanish music that is normally played on a flamenco guitar (with special strings) and originated from Andelusia, a district of Spain. There are many styles of Spanish music, not just flamenco.

Occasionally the term "finger style" is used to differentiate between the use of simple three chord strumming and the more complex picking of a melodic accompaniment or solo.