This is the instrument most people think of when they think "guitar". An acoustic guitar is hollow, and almost always has a "sound hole" - a round hole in the face of the guitar. Acoustic guitars almost always have six strings. When you strike the strings of an acoustic guitar, the instrument produces a rather loud sound. Although acoustic guitars are often associated with folk music, and "mellow" music in general, they are in truth in all styles of music, from country to blues to heavy metal.
A "classical guitar" looks quite similar to an "acoustic guitar", and is indeed still an acoustic instrument, but it has several distinct differences. Standard acoustic guitars have six strings made of steel, whereas classical guitars have six strings, three of which are nylon. This produces a sound quite different from an acoustic guitar. The neck of the guitar is also much broader on most classical guitars. I'll go out on a limb and say that unless you are interested in focusing on classical music, this style of guitar probably shouldn't be your primary choice for a first instrument.