pezhetairoi: It allows you to force an AI faction to accept a proposal made by your diplomat.

Dyabedes of Aphrodisias: Are you clicking the "show me how" button when the negotiation screen is up, or did you do it before your diplomat started the talks? If you did everything right then it may be that the AI faction doesn't have enough money to fullfil your demand, or doesn't think that it's income in the future will suffice. (Remember that in EB the factions economy is mostly based on scripted free money, and the AI doesn't know it's going to be getting all those freebies. And it doesn't know how to disband units either, so it probably looks at it's income/outcome calculations and thinks that it'll be broke soon, like most player-controlled factions will become without disbanding expensive units/fleets.)

Also, it should be mentioned that RTW has/had a bug (not sure if it's been fixed) whereby if you failed a negotiation (for what ever reason) then all further negotiations will automatically fail until next turn.