Multiple independently targetable reentry vehicle
Multiple independently targetable reentry vehicle (commonly called simply MIRV) is a practise of placing more than one nuclear warhead on a ballistic missile, each of which can be aimed at a different target. The Soviet Union wanted to ban MIRV's as early as the late 60's (during the SALT I talks), but when President Richard Nixon started production of the MIRVed Minute Man III in 1971 the Soviet Union refused to discuss MIRV technology. The Soviets soon had a MIRVed missile of their own: the enormous SS-18.
Implications of MIRVs
The production of MIRVed weapons lead to several national security policy dilemmas. Since multiple warheads can be placed within a single missile, there is no way for a power to know the total warhead capability of its enemy, short of physical inspection. This forces the country to assume that there are as many warheads per missile as physically possible, which can lead to an overestimation of an enemy's capacity.
MIRVs also destabilize nuclear deterrence. The sheer number of warheads can cause worry about strategic vulnerability. It also means that a first strike country will have a tremendous advantage, especially since MIRVs have a lower circular error probable radius, which gives it a better chance that it will be able to destroy enemy nuclear missiles in their silos.