A Virtual Private Server (VPS) is a slice of a real physical server, isolated from other tenants by hardware virtualization (KVM, Xen, or a similar hypervisor). The tenant gets a guaranteed CPU/memory/disk allocation and full root access to a Linux (or Windows) install, billed by the month. Modern VPS plans start at $4-7/mo for 1-2 vCPU and 2-4 GB RAM, which is enough to comfortably self-host most single-purpose OSS applications with room for a database and a reverse proxy on the same box.
In a self-hosting context
For 90% of the self-hostable SaaS replacements in this directory — Mattermost, Nextcloud, Gitea, Plausible Analytics for a small team — a single $5-15/mo VPS is the right amount of hardware. See the VPS providers compared comparison for the six providers we track on price, EU data residency, and free tier. For larger workloads or anything bandwidth-heavy, see Bare metal.