Dayworld is Earth in the future. World leaders have instituted a new way of living to solve overpopulation. The days of the week exist as alternate realities. Each day has it's own police, firemen, government officials, doctors and people. Most people share thier homes with seven other people, couples or families though never see each other. The 'stoning' device allows all this to be possible. A person or object may be placed in suspended animation for any ammount of time, then reactivated at the desired time. So, a person who lives on Monday would enter thier stoning chaimber before midnight, and then be reactivated the next Monday at midnight with no perception of the time that had passed.
However, a secret society, the 'Immers' is working against the government to allow people to live all the days, and to have freedom and democracy. They employ 'daybreakers' in thier fold who commit one of the ultimate felonies to bring messages to agents who exist in the different days. Jeff is one of these. He has divided his personality into seven distinct personalities, one for each day as a controlled skitzophrania. But, events which threaten him and his society cause his personalities to come crashing together and may threaten to destroy him and the Immers.
Overall, a good book. The charachterization was good, though not as in depth as it could have been. And, it seems from this book and others of Farmers books I've read he doesn't write strong female charachters to take stronger roles.