Oracle, like other RDBMS', has the ability to import and export databases. In Oracle10g this system was significantly overhauled and dubbed "Data Pump". More can be found about this in the Oracle Database Utilities manual.
Data Pump provides the ability to export in several modes, including Full Export, Schema, Table, Tablespace, and Transportable Tablespace. Exports are "logical backups", which means the essence of the instance is exported but not the frame work.
As an SA, exports feel like a real "pack your shit and go" operation. Think of leaving an office, you don't take the desks or drawers (tablespaces, control files, etc), you just empty the contents into a big container (dump file) and leave. The result of an export is a dump file. The file is binary and effectivly just contains a pile of INSERT statements that when imported updates the instance. Because of this you can't import a dump without a database instance ready to accept it, just as you can't unpack your stuff into a new office unless it has a desk and drawers similar to the one you just left. Therefore you can't really look at an export as a serious backup method. It's a great way to cover your ass or to move data from one place to another, but it's not much diffrent than just writting a PERL or PL/SQL script to output every table into a flat file and then using SQL*Loader to CREATE and INSERT everything back into tables. "Recovering" a database would invole creating a new instance of the database from scratch (using dbca for instance) and then importing into that new instance.
With the limits of Data Pump exports understood, there are some advantages to exports. Because you are importing data into an existing instance you can easily move tables, tablespaces, schemas, etc into other databases. Furthermore, because the data is fairly generic, it provides a solid method of migrating from one version or Oracle to another (if needbe). I've seen several DBAs take exports just before applying major patches, just as a failsafe.