Apple's Xserve is pretty expensive and not really targeted at individual users, but it is really just a file server. It acts like another Mac with file sharing turned on where you can create an account and mount its drive to your Mac. The reason for the high price is that it is designed with redundant hardware so that if anything breaks, it can keep running on a spare until a convenient time to get it repaired. Its local disk drives are configured in RAID arrays so that if a drive dies, its information can be rebuilt based on the information on the other drives. It has hardware support to connect to a Storage Area Network (SAN) to provide even more storage. It has multiple power supplies each with separate power cords. But if you take out all of the complexity from the redundant hardware, file servers are really the least complicated kind of server there is.
You can duplicate the functionality of an Xserve for home use with a second Mac or Linux computer with file sharing turned on, or even with a dedicated Network Attached Storage (NAS) box you can buy for under $500.