A tablespace is a designated location on a parition to store database objects such as tables and indexes. They are often used to spread a large databases over multiple logical partitions to improve performance.
The host bus adapter is what connects your computer to your storage/discs. Often a SCSI, iSCSI, SAS. Fibre Channel or a SATA card depending on your storage type. This card controls how your disc is configured and set up with regard to RAID levels (If you have a RAID capable card) (Redundant Array of Independant Discs, typically mirroring/striping or striping with parity RAID 1, RAID 10 or RAID 5)
http://en.wikipedia.org/wiki/RAID talks more about RAID levels and what they mean.
RAID arrays are typicaly transparent to your OS, so your OS doesn't care about the RAID level, only the HBA does.
RAID allows you to configure redunancy in your disc array, so that if one disc fails, there are others with the data on it so that your server doesn't go down and you don't loose data (which is what I suspect you want). A RAID array is managed purely by the HBA (at least in the case of hardware RAID, which is what you want because it supports Battery Backed Caches), and doesn't affect how the OS sees the disc. And seeing that postgresql makes calls to disc through the OS, if the OS doesn't care, neither does postgresql. The thing you have to be carefull of is drivers for your HBA in the OS. Many HBAs have very poor drivers, especially for Linux and other UNIXes, so you can often see very bad performance because of a poor HBA driver.