This policy reduces the rate of war weariness accumulation and provides garrisoned cities with a Loyalty bonus that increases in each expansion. It's invaluable for warmongers making a late-game push toward a Domination Victory, and all but ensures that Cyrus, the Zulus, and the Ottomans won't have to assign Governors to the cities they capture in order to hold them.
Martial law is that legalism by which military law “temporarily” supersedes civil law, declared by a government whereby it doesn’t have to worry about such niceties as civil rights, habeas corpus, civil courts (civilians defying martial law can be tried by military tribunals), and can impose curfews, travel bans, rationing, and such at will. In effect, all power is transferred to the military, and is removed from the previous executive, legislative, and judicial authorities (some of whom may well be imprisoned themselves). There are many potential reasons for imposition of martial law “to restore order”: following a coup (as in Thailand in 2006) or a natural disaster (the San Francisco earthquake), perhaps during labor unrest (the Colorado Coalfields War) or war (as in Hawaii from 1941 to 1944).