While there might have been a server that advertised those specifc features, it is just a file server with backup software and configurations, there is no specific box from company X that is what everyone uses for this.
I am going to go into some basic information on the different aspects of this question, sorry if it gets lengthy.
The mirror your boss is referring to is most likely a RAID array, RAID 1 to be exact (there is RAID 0, 1, 3, 5, 6, 1+0 /10). RAID 1 is called a mirror, it is an exact duplicate so you have 2 drives that are perfect copies. Now many people are confused by this and think that RAID 1 is a backup solution; RAID 1 gives you duplicate in case of drive failure, but if you have a file corruption or windows infection then all RAID 1 gives you is a perfect copy of the same corruption/infection.
The reconstruct a file portion sounds like what is called versioning or shadow copy. What it does is that it reads the file is changed and saves the previous version of the file (often in a hidden folder to be transparent to the user). This way you can revert back to the old version of the file.
Now you said medium sized business but that means many different things to many different people. How many PCs/users and how many servers are we talking about and are you using a windows domain server (if so you can log in as any user at any work station). The other big thing here is are your users all using files/programs that are mostly on their individual PCs or shared files/programs on a server?
Generally you would have your shared resources backed up and maybe the user files backed up depending on situation.
It is also a good idea to either do a full hard drive disk image backup of the PCs or if all files are stored on a server and all PCs are the same model with the same software then you can have one default disk image to apply in case of a failure.
If we are talking about 2-8 PCs and a server or two with only a few shared programs I can talk you through what you need. If we are talking a lot beyond that then your boss has to big of a business to expect a employee to just slap it together, you need a qualified professional on site to setup everything and really look at what your needs are.