Here's a hint: It won't be picking out a new china pattern, or final approval for all floral arrangements. It also won't be a co-president and Bill won't be attending cabinet meetings.
The NYT has some ideas,
Unlike Mrs. Clinton, who was new to Washington when she became first lady, Mr. Clinton brings a wealth of political relationships, untold diplomatic experience and vast firsthand knowledge about issues and crises that presidents face. He could easily be deployed to make discreet phone calls to governors, members of Congress and business leaders, or to play a role in negotiations between foreign leaders or in global hot spots.On that latter part, I wouldn't bet on it. Say what you will about the Clintons, they've often been their own worst enemies, they have stayed together all these years for some reason. When they left the WH, nothing stopped Hillary from leaving Bill; she could have done so without any political price, but here we are.
Mr. Clinton would not necessarily be at the White House full time, advisers say. The couple would most likely keep their home in Chappaqua, N.Y., and Mr. Clinton might continue doing some work in Manhattan with his foundation or at the offices he has kept in his post-presidency.
When in Washington, he would be less likely to be a social planner for his wife than to be her protector within the White House. Some friends of the Clintons said they could see him taking a page from Nancy Reagan, who could be aggressive in ensuring that administration staff members were serving the interests of President Ronald Reagan. Mr. Clinton might know better than most if Mrs. Clinton was being overburdened or receiving bad advice.“He’ll be her advocate, he’ll be her lawyer, and if he thinks the staff isn’t protecting her, they’d have private conversations about it,” Mr. Kantor said. He said, however, that he did not think Mr. Clinton would go as far as Mrs. Reagan, who orchestrated the ouster of Donald T. Regan as White House chief of staff.
Read the Times piece. It's interesting and I think well done.