Multi-tenancy is a way of building software so that a single running application serves many separate customer organizations at once. Each customer is a tenant, and every tenant's data is partitioned so it stays completely private from the others.
The way to picture it is an apartment building. Everyone shares the same structure and the same maintenance crew, but each unit is locked and separate. Sharing the building is what keeps costs down. The locked doors are what keep tenants apart.
That sharing is why SaaS costs so much less than software of the past. One application serves thousands of businesses, spreading the cost of hosting and engineering across all of them. Isolation is usually enforced down at the database level with row-level security, which makes it technically impossible for one tenant to reach another's data.
When you size up a SaaS vendor, how carefully they implement multi-tenancy and data isolation is one of the most important security questions you can ask.