Opportunities to network with fellow administrative professionals and participate in local educational programs.
Awareness that it isn't "just a job" -- it is a career and you're in control of it and responsible for it.
Exposure to other professionals outside your company to help expand your interpersonal skills and comfort levels -- you can call upon a network of professionals to determine the best way to accomplish a task or receive advice -- so you don't have to keep reinventing the wheel. In addition, the IAAP global network is very useful when execs are going to other cities and/or countries and you can contact an IAAP member for information about a particular area.
Leadership opportunities through participation in chapter activities (can be everything from public speaking, to project management, to strategic planning, to event planning -- skills you might not learn on the job or through training provided to admins by employers).