SSAS is an OLAP database, where OLAP stands for Online Analytical Processing.
A relational database not used as a data warehouse is an OLTP database, where OLTP stands for Online Transactional Processing.
OLTP is more concerned with fast updates, deletes and inserts and deals with a lot of small transactions.
OLAP on the other hand, is more concerned with a lot of reads (for reporting) and much less with inserts or updates. So basically there are two completely different scenarios.
Although you can just build a data warehouse in SQL Server using dimensional modelling (which you probably have done so far) to cope with the amount of reads, SSAS has some extra advantages.
SSAS allows you to build a model (multidimensional in SSAS 2005/2008/2008R2/2012 or tabular in SSAS 2012) which is put on top of the data warehouse. SSAS is designed to store data in a different way, making it fast to read (SSAS is essentially read-only, unless when you process your cube). The biggest reason SSAS can be faster because it pre-aggregates some of the data. For example, suppose you have all your facts at the day level, but your reporting is at the month, quarter or year level.
If you'd want to calculate the measure for the whole year in the data warehouse, you'd have to do 365 calculations (each for every day of the year). SSAS on the other hand, would pre-aggregate the data to the month level. If you'd need reporting at the year level, SSAS would need only 12 calculations. At the quarter level, only 3 and if you would report on the month level, no calculations would be done at all.
There's of course much more to SSAS then just simple aggregations, so I would suggest you try to pick up some books. Also determine if it is worth investing your time in SSAS Tabular (introduced in QL Server 2012 and it stores data in tabular format and in-memory, making it usually easier to develop your model and it's blazing fast in some scenarios).
Also try to learn about dimensional modelling, if you haven't already: The Data Warehouse Toolkit: The Complete Guide to Dimensional Modeling
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