Containment is geared toward helping you displace the Suzerains of city-states. It works particularly well if you're leading in civic development and have adopted a government that your opponents haven't unlocked yet...and, in Rise and Fall and Gathering Storm, in conjunction with Spies who can perform Fabricate Scandal missions to further tip the balance in your favor.
Civilopedia entry Edit
As the Cold War opened, the United States opted for a policy of “containment” of the Soviet Union, the “evil empire” of communism. George Kennan, a career Foreign Service officer, formulated the policy which became the basis of the Truman administration’s response to threatened communist expansion. It was controversial, to say the least. Eisenhower refused to intervene in the Hungarian Uprising in 1956, but Johnson used it to justify American involvement in Vietnam. Nixon and Kissinger rejected it completely in favor of working towards détente with Russia and China through expanded trade and cultural exchanges. Reagan returned to the strategy by sending aid to a variety of anti-communist insurgents, notably in Afghanistan, leading to the eventual collapse of the Soviet Union.