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Basically, the higher the number, the greater the level of redundancy and compartmentalization. There is a nice, plain English summary at cybercity.biz.
Tier 1 - Non-redundant capacity components (single uplink and servers).
Tier 2 - Tier 1 + Redundant capacity components.
Tier 3 - Tier 1 + Tier 2 + Dual-powered equipments and multiple uplinks.
Tier 4 - Tier 1 + Tier 2 + Tier 3 + all components are fully fault-tolerant including uplinks, storage, chillers, HVAC systems, servers etc. Everything is dual-powered.