Exec-in-Charge has two definitions based on the context.

Blues Pub

With respect to Blues Pub, the exec-in-charge is the member of the Executive Committee who supervises Blues Pub and deals with any major issues.

EUS Groups

With respect to EUS Groups, the exec-in-charge is the member of the Executive Committee whose portfolio your group falls under. Their job is to oversee the general goals and performance of your EUS Group. Not all EUS Groups have an exec-in-charge for example Departmental Societies.