Amphora means 'to carry on both sides'. These jars had 2 handles and were used to store and carry liquids and solids.  

Black figure ware (black figures on a red background) was particularly popular in Greece 600 - 500 BC.

The musical instrument depicted on this amphora is called a kithara. It's a type of lyre, with seven strings of equal length and a wooden body, usually with a flat base. The musician playing it was known as a kitharode and these instruments were usually reserved for public performances.