Functionalists believe that every aspect of society plays a role in keeping society stable. Therefore, they argue that stratification does this. They say, for example, that stratification increases stability by preventing people from moving out of the social group that is occupied by friends and relatives.
By contrast, conflict theory argues that aspects of society come about through conflict between groups. They would argue that stratification is caused by members of the dominant group winning out in the conflict with other groups. The dominant group then imposes stratification so as to be able to keep its dominant position.