A traditional monolithic database assumes that you have locally attached storage. All of your ingest, indexing and query processing happens on the machine with that storage (i.e. your compute and storage live together). The cloud kind of complicated things with EBS and high IOPS network storage, but generally, those work kind of the same way. The volume is mounted on a single machine that uses it.

When people talk about separating compute from storage, they mean pulling compute heavy tasks like query, ingest, indexing, and compaction apart and using a shared storage tier that many systems can talk to. Usually this is object storage paired with some sort of catalog (kept in either object storage or some other store or API).

Snowflake popularized this approach in the data warehousing and OLAP space with great success. Their papers submitted to VLDB are great reads on the topoic.