Bare metal hosting means renting (or owning) a whole physical server, with no hypervisor between your operating system and the hardware. The trade-off versus a VPS is more total CPU, memory, and disk per dollar at the cost of less elasticity — you cannot resize a bare-metal box in 30 seconds the way you can a VPS, and recovery from a hardware failure is on you (or the colocation provider). Hetzner, OVH, Latitude.sh, and Equinix Metal are the popular bare-metal vendors for self-hosters who outgrow a VPS.

In a self-hosting context

Bare metal starts paying off for self-hosters when CPU, RAM, or disk I/O becomes the bottleneck — for example, a Mattermost server with thousands of concurrent users, a Plausible Analytics install ingesting tens of millions of pageviews, or any workload that needs >32 GB of RAM. For everything below that threshold, a VPS from one of the providers in VPS providers compared is fine. See Containers vs VMs for the trade-off in the other direction.