High level:
In a ROLAP environment, SQL queries are sent to a database on an RDBMS, the result is returned to a middle-tier server for final cross-tabbing and formatting, and then sent to the client that initiated the query.
In a MOLAP environment, multi-dimensional "cubes" (often greater than 3 dimensions) are pre-calculated on the middle tier from one or more source systems and stored in a proprietary format. End-user queries are run against the cubes and not the underlying databases/RDBMS's.
There is far more detail, nuances, overlap, and hybridization of ROLAP and MOLAP. I know there are scores of references out there. You can start by doing a key word search in Google.