What advantages does in-memory OLAP have over traditional systems with significant memory?

Not my field of expertise but as I understand it the difference in the majority of so-called in-memory OLAP databases (not a term I'm fond of, it's used as marketing pitch more than as a fair comparison of technologies) is column store indexes.

Column-Stores vs Row-Stores (How Different Are They Really) is a good intro to the technology if you're familiar with traditional OLTP and OLAP database structures.

Column store indexes will make an appearance in SQL Server 2012 (aka 'Denali').

Here is a link to a Power Point presentation by Conor Cunningham, Principal Software Architect in the SQL Server Query Processor team covering this new feature.

Databases designed with the assumption that they will be entirely resident in main memory can use structures such as T-tree indexes. But the real advantage is, IMDBs are just simpler. They do less (as they don't have to worry about managing a cache, or serializing writes for consistency, or anything to do with ACID-compliant I/O at all) so they execute fewer instructions on the hardware to carry out the same "work". A general-purpose database has to be all things to all people; like a Leatherman has a dozen tools, but sometimes you just need a cutting edge, so you buy a blade from Cold Steel, and no-one debates that it is a better knife!