BC means Before Christ, and AD means Anno Domini, which is Latin and means 'in the year of our lord' (ie, year of God).
These terms are derived from the Gregorian Calendar, which is known in most of the world and used in the majjority of countries with a Christian heritage, and the slightly different Julian calendar, which is used in some Orthodox Christian countries, notably Russia.
Both terms are based on a calendar which was created in the 6th century by a monk called Dionysius Exiguus. It is derived from the year that Jesus was born as far as this could be known. Years BC are counted backwards from this date, so 1 BC is a year before Jesus' birth, 2 BC is two years before etc. There is no '0' year in this calendar, so 1 AD is 1 year after 1 BC. This has caused some argument in the past.
You can learn more about this here.