An executive is a powerful person who is responsible for making things run in a planned manner. In LaraOffice the executive is the organ exercising authority in and holding responsibility for managing the working of the organization. He has the authority and responsibility to execute and enforce laws regarding the organization.
The main difference between Admin and Executive in LaraOffice is that the executive cannot have a multi delete option. The executive has authority over all the modules that are given to admin.
To have more details about the working of the modules go through the link.