The Governor and the Executive Council
The Governor signs or vetoes. The Council -- five members, elected by district -- approves contracts, nominations and pardons, and almost no resident could say what it does.
The Governor is elected for two years, at the same election as the whole legislature. When a bill has passed both chambers the Governor may sign it, veto it, or do nothing — in which case it becomes law without a signature.
A veto is not the end
The legislature can override a veto, but it takes two thirds of the members voting in each chamber. That is a high bar and most attempts fail.
Across the two terms on this site there are 68 vetoed bills. In 58 the override failed. In 9 it succeeded and the bill became law over the Governor's objection. One was still awaiting its override vote when this was written.
When the Governor vetoes a bill, the reasons are set out in a message read into the record of the chamber the bill came from. Those messages are printed in the House and Senate calendars, and this site carries 67 of the 68.
The Executive Council
Five councillors, each elected by district, meeting with the Governor. Almost no state has anything like it, and almost no resident could describe what it does.
Its consent is required for a great deal of what the executive branch does: state contracts above a threshold, the appointment of commissioners and judges, and pardons. A Governor who has the legislature and not the Council cannot simply proceed. This is the concrete answer to what the Council is for — a commissioner nominated by the Governor takes office only when the Council confirms them.
The Council is genuinely debated. Supporters say it is a check on executive power that no single elected officer should be without. Critics say it gives five people a veto over routine administration and slows work that has already been authorised. Both are arguments about the same fact.
This site indexes the legislature, and it holds almost nothing about the Executive Council: no agendas, no contract votes, no nominations. What it does hold is the legislative half — the vetoes and the override votes, linked below. For the Council's own record, go to the Council.