This phrase is used in dating because of the dominance of the Christian faith in Europe. The phrase "Our Lord" refers to Jesus Christ. Christians believe that Jesus Christ was born 2010 years ago this year. He is referred to as "our Lord" because Christians believe that he is God -- a part of God.
So our dating system is based on the date that Jesus is believed to have been born. We more typically say a year is, for example, 1974 AD. AD stands for Anno Domini, which is the Latin for "Year of Our Lord."