Laity are members who do not hold the Priesthood but may play an important role in the running of their local church. The responsibility of Primary usually falls to the women, as does the Young Women. Worthy males are responsible for the Young men.
As a Mormon, a local Ward of the church will require 120 of its members to see that all of the needs of the Ward are met. The ages range from eight year of age onwards. To give an example A Primary class of eight year old's will have a Teacher, as Class President and two counselors if required. This same organization runs through out the local Wards and Branches from the Bishopric or Branch Presidency. Of course this will depend on the number of members in each Ward or Branch. So you can see Laity represent an important part in the running of the local church. The Vicar, Bishop or whoever the leader is cannot do it all by themselves.