Local deployments is a game setting that changes the way that armies may be deployed. When enabled by a game creator, armies that are earned from a bonus may only be deployed to the territories within that bonus.
When your income is reduced (by, for example, negative bonuses, army cap, or sanction cards), the reduction in income will be spread out amongst all deployment options evenly. For example, if you have a bonus worth 3 armies per turn, 5 base armies per turn, and a bonus worth -2, the -2 will take one away from the 3 bonus armies and one away from the 5 free armies.
This setting cannot be used with overlapping bonuses, such as superbonuses. If you want to use this setting on a map that has overlapping bonuses, you must override one of each overlapping bonuses to 0 or negative, so that no territories belong to multiple positive bonuses.