Premium bandwidth can be understood as partnerships that host makes with some high quality bandwidth carriers or providers. Such carriers are measured using tiers, ‘tier1’ being of the highest quality.
A Tier 1 carrier operates and owns their physical network. This network would have a peer network with other tier 1 networks. One such example is AT&T. Some lower networks such as tier 2 might have regional networks. These might resell these connections to tier 1 networks.
Because of the cost involved, they would generally oversubscribe/ oversell the connections. The over-subscription would continue since it is resold from one level to the other before reaching the end user.
Ideally, hosts offering premium bandwidth, purchase it directly from tier 1 providers. They then sell the connection to a network. Mostly they are backed by a solid network that offers a high level of availability.
The best thing to do, if you happen to meet someone, promoting ‘premium bandwidth’ is to ask them what it means, as it might be quantified differently by different people.