If you get awarded the contract to do something, but you can't do everything that's required, you can sub-contract with a different company. For example, I might employ a master builder to make me a new house, and I pay him, but he arranges to have an electrician, a plasterer and a kitchen fitter come and work for him for a few days each.
This idea of services being provided by people at different levels of subcontracting can be considered tiers... like the tiers in a wedding cake.
At the top level (tier zero, if you like) you have the main contractor. He employs the kitchen fitter, and I don't necessarily have to know anything about it. The kitchen fitter is tier 1, and is chosen by the guy at tier 0. If the kitchen fitting company decides they need a specialist to do some tiling or something, they will employ a tiler for a day or two... and that's tier 2.
In the gulf oil spill scenario, BP is at tier zero, Transocean Ltd is a tier 1 contractor, and anybody who supplies goods or services to Transocean is tier 2. For example, maybe Hyundai Heavy Industries, who built the Deepwater Horizon drilling rig.