Classical languages
In European culture, the phrase classical languages refers principally to two dead languages and their literatures: Latin and Greek; and it is from these two languages that many of the words in today's English language are derived (see, for example, Latin in the History of English and other pages in the Outline history of the English Language). Latin was the language of ancient Rome (the Roman Empire), about the time of the birth of Jesus Christ. When we use the names of the two languages together like this, Greek means the language used in ancient Greece, at the time (before the birth of Jesus Christ) when it was the centre of European civilisation. These two languages are so important in the history of European scholarship that they are called the classics.
The classical languages are dead languages in that they have no living native speakers. Indeed if they are spoken at all (as a second language) they are unlikely to resemble the original language to a great extent due to the fact the spoken language will have a large amount of variation from its original roots.
The importance is that they were the language of all education higher than Primary school, throughout Europe. This was particularly true of Latin, which was the language of instruction in universities from their beginning to after the Reformation of the church, in the 16th century. (The 'grammar' studied in Grammar Schools was the grammar of the Latin language, and this period of education was designed to prepare young men - no females were included - for University.) Greek was less known. Indeed, it was hardly studied in western Europe from the fall of Rome, as the centre of the Roman Empire, until the capture of Constantinople (now called Istanbul) by the Ottomans in 1453. After that, the importance of the ancient Greeks as the originators of a great deal of modern European culture began to be recognised, and studied in great depth. This is why Latin and Greek are sometimes called the learned languages - they were the languages of learning, understood by all educated people.