As a historical period, it is the period of time between about 1750 and 1815. The beginning of the classical period of music was marked by the death of Johann Sebastian Bach. It is characterized by very simple melody lines over a basic accompaniment, often utilizing motifs and sequencing with strict structure and form applied. The Grand Daddy of the classical era is considered to be Joseph Haydn, who has been given the nickname's "Father of the String Quartet", and "Father of the Symphony". Ludwig van Beethoven is also a prolific composer from this period of music, though Beethoven is given more credit for being the leader of the transition into the Romantic period, due to his odd ways of composition which became noticeable has he lost his hearing.
In general terms, classical is used to characterize music written before what is considered to be the contemporary genre of music, specifically music written before 1915. Suffice it to say that it takes an enormous amount of skill to be a classically trained musician. Listen to the Chopin Scherzo in B-flat Minor, or the Beethoven "Waldstein" Sonata. For more recent "classical", listen to Prokofiev, or even the wonderful Gyorgy Ligeti, who died recently in 2006. Classical music is very much alive and it is the reason we have the music we have today. And don't do what a stupid youtuber did once and tell someone opera sucks, therefore Justin Bieber has more skill than a Soprano soloist singing Mozart operas.
Anything Mozart, anything Haydn, and thousands of other composers, including Beethoven before he was about 30, is considered Classical Music.