It was essentially a compromise. When the UN Charter was first being drawn up the Soviets had argued for a limited membership, one restricted to the 1942 signatories of the UN Declaration. A broader membership, which the US was pushing for, would potentially see the Soviet Union permanently outvoted by the Western client states and colonial dominions. As the negotiations dragged on, one of the Soviet demands became the admission of all sixteen constituent Soviet Republics to the General Assembly.

The eventual compromise saw broad membership be adopted but also strengthened the Security Council and permanent members’ veto. This gave Stalin some assurance that the new body wouldn't become an anti-Soviet vehicle in any meaningful sense. As part of the deal the Soviets also got two of their republics (in addition to the USSR proper) admitted to the General Assembly, thus strengthening their bloc in that chamber.

Source: Mark Mazower, Governing the World