Is Tablespace something like Logical Volume?
Historically, PostgreSQL stored tables and indexes in individual files.  Tablespaces are a means of placing multiple tables/indexes into a single file or group of related files in the same directory.  Other database management systems use similar techniques, although tney can store multiple objects within a file.  On PostgreSQL a tablespace is implemented as a directory that individual files are placed in, but the files are still one-per-database-object.

A table must reside in a single tablespace unless it is partitioned, in which case each partition must reside on a given tablespace.  On some DBMS platforms you could add files to a tablespace as you suggest, although in the case case of PostgreSQL a tablespace is essentially just a directory for grouping files together.  On systems where this is possible it could result in suboptimal I/O performance as individual disks could contain I/O hot spots.  Probably, you would be better off setting multiple disks up in a RAID volume and placing the tablespace on that.

Depending on your workload you may wish to set up individual disk volumes with tablespaces on each volume and distribute parts of your database over the different volumes.  The most trivial case is separating database logs onto a separate volume, but you could distribute data over multiple volumes for various reasons.

EDIT: Here is a link on PostgreSQL tablespaces.