Construction supervisor
In short
The supervisor is "your eyes on site". They work for you, not for the contractor: checking each stage is built correctly, approving payment only for work done, and documenting everything.
The professional explanation
Responsibilities: reviewing drawings before execution, quality control at critical stages (foundations, reinforcement, waterproofing, systems), approving interim invoices against the bill of quantities, keeping the site diary, checking changes and extras, accepting works and coordinating consultants.
Supervision differs from project management: a project manager leads the whole process (design, licensing, contractor tender, budget); the supervisor focuses on execution. In small projects one person often fills both roles.
Supervision cost is usually a percentage of construction cost or a monthly fee, and typically pays for itself in avoided extras, errors and delays.
Example from the field
On a house in Kfar Saba the supervisor spotted, before pouring, that beam reinforcement did not match the structural drawings. Fixing it before the pour took hours; after the pour it would have taken weeks and demolition.