Keep in mind that Hydra is a whole suite of protocols, some of which are still in the research phase.
On Hydra Head specifically, you can think of it as a protocol for creating and maintaining fully composable and dynamically available state machines between willing participants, with snapshots being periodically committed to the CSL.
Participants of the Hydra Head are analogous to SPOs; except they are tasked with maintaining consensus only on the state of the head. Depending on the size, scope, and function of each head, the consensus and ledger mechanics may greatly differ between some head protocols, but will nevertheless be settle-able on the main chain. Additionally, the Hydra Inter-head paper describes ways to create channels between heads without having to close them or pre-settle on the CSL.
Hydra Tail is an upcoming paper that, according to the having-read-about-it-long-ago whispers of my mind, describes how individual head participants can offer centralized services to individuals. (i.e. I, as a lone L2 state operator, can offer you and many others some sort of service on my machines).
People with thin clients/mobile devices in remote regions would be able to transact through a single or small handful of trusted operators.
This would in effect, create the first fully interoperable stack of protocols across the ENTIRE length of the THROUGHPUT -------- DECENTRALIZATION spectrum. For the first time ever, we'd have a family of protocols that make the security of a decentralized settlement layer and the throughput of a centralized compute layer interoperable.
