On a shared machine, a single misbehaving process can slow down or crash everything else. Isolation puts each workload in its own boundary, with its own limits. The tools include separate user accounts, per-process limits, Linux control groups, namespaces, containers and virtual machines. The stronger the boundary, the less one compromised or runaway component can affect the rest.
For web hosting, this might mean running each site's PHP workers under its own user and pool, with its own memory limit, so that a problem on one site does not take down the others. It also limits what an attacker can read after breaking into one site.
Isolation has a cost in complexity and in overhead, and it is not absolute. Containers share the host kernel, so a kernel flaw can cross the boundary, while virtual machines give a stronger separation.
Decide which pieces matter most, such as admin interfaces, databases and public sites, and give them separate boundaries and limits before an incident forces the question.