I think this means the director does not have to obtain approval for decisions from a management team, whereas a two-tiered management structure consists of a "Board of Directors and a Management Team" as described below.

What is a Proprietary Limited company?
For legal purposes, a company has a separate legal existence, which is distinct from its owners, managers, operators, etc. It also has its own income tax liability, separate to your personal income tax.
As mentioned, there are two types of companies, proprietary and public. Under the governing Corporations Act, a proprietary company must either be:
A proprietary company must have at least one director who must live in Australia. On the other hand, a public company must have at least three directors and of these, at least two directors must ordinarily live in Australia.

http://au.smallbusiness.yahoo.com/040202/7/e3c.html

One of the major weaknesses in the corporate governance framework in Bulgaria is the minimally defined level of responsibility for members of the supervisory body. Under the CL, companies may choose to have either a two-tiered or a unitary board of directors; under a two-tiered structure, all (supervisory) board members are chosen from outside company management. However, under both a two-tiered and a single-tiered structure, Bulgarian companies tend to be run by company management with little supervisory review by the board of directors.
http://www.worldbank.org/ifa/BulgariaROSC.pdf

LB Icon has a two-tiered management structure, consisting of a Board of Directors and a Management Team.
http://www.iconmedialab.com/corporate/executive.asp