Well, I'll take a crack at this...
BSD is basicly a version on UNIX in the same way that LINUX is basicly a version of UNIX. In the 80's, it was called BSD UNIX. It lost the legal right to call itself UNIX sometime in the '90's. The UNIX trademark is owned by the Open Group and they now decide if an OS may officially call itself "UNIX". Neither BSD nor LINUX has been blessed by the Open Group. (See
What is UNIX?.)
BSD has been around a long time. It is the source of the entire sockets interface, the TCP/IP protocol stack, reliable signals, vfork(), select(), syncronous I/O, and secondary group membership. And they originated some non-kernel stuff too, like csh, vi, and sendmail. Without BSD, Unix would be a very different OS.
My first unix system was a System III, but the the vendor prominently claimed "with Berkeley Extensions". I think that was roughly 1979.
There are 3 viable distributions of BSD:
NETbsd,
OPENbsd, and
FREEbsd.
I have to say that I find the BSD's to be rather alien. In contrast, I feel quite at home on a Linux system. But that is just one man's opinion. We have all three in operation at work. I don't work closely with any of them, but here is my impression of each...
NETbsd will run on any platform. It may be the most portable real OS ever written. For many systems, it's the only game in town. And it has a reputation for being easy to install. It is very stable and very fast. It would be the a good choice for a very heavily used ftp server or web server.
OPENbsd is a very secure OS. The only OS's more secure are military grade and propietary. It is tough to install and does not run on many systems. But it can safely be directly connected to the Internet. So for systems that must be outside a firewall, like nameservers or ntp clients, OPENbsd is the best choice. And it also is a good choice for running a firewall.
FREEbsd also does not run on many systems. And it is not an easy install either. But it has a reputation for being easy on end users. Apple's OS X has a version of unix called "darwin" which is actually FREEbsd. FREEbsd would be a good choice for a workstation.