The BSD license is one of the more popular free software/open source licenses, first used in the BSD releases by the Computer Systems Research Group at the University of California in the late 1970s. From there it spread through 386BSD, and then FreeBSD, NetBSD, OpenBSD, and (later) MacOS X. In addition it is reasonably popular among other communities of software developers; based on information gathered from freshmeat.net and SourceForge, BSD is currently the third most popular license for free software, behind the GNU GPL and LGPL. The BSD license is in many ways the license most like the public domain; the only restriction placed upon you by accepting software that uses this license is that you can't hold the author(s), contributor(s) or anyone else liable for the software if something bad happens. If you want to modify it and sell binary copies - fine. If you want to fork a version and GPL that fork - go right ahead. Anything goes with BSD.
There seems to be two schools of thought about how 'free' the BSD license is. One group says that it allows commercial interests to lock away the code (or at least their forks of it), and that this means BSD is less free than the GPL. The other group says that this is why the BSD license is more free than the GPL; it gives you the freedom to lock away the code if you want, sort of like how the First Amendment protects hate speech even though nobody really likes it that much†. Essentially, the BSD license offers more freedom to developers, and the GPL offers more freedom to users. This is one reason why the BSD license (or close relatives) are commonly used with libraries performing things like cryptography or data compression; it is considered more important for people to use the right technology (be it deflate compression, or a good cipher), even in closed source software, than it is to encourage open source. This is usually implicit, but the creators of the Ogg-Vorbis audio compression format made a point out of it; they felt it was far better for everyone to move away from the heavily patented MP3 format to their own (unpatented) format, and the best way to encourage that was make their encoders and decoders free to use in commercial software.
The BSD license has a few variations introduced over the years, mostly removing conditions from the already short list. First, we have the "original" or "annoying advertising clause" version of the license. This variant is incompatible with the GPL, as the GPL forbids adding extra restrictions beyond what the GPL itself imposes. This can be highly problematic for software that wishes to make use of both GPLed software and software under the original BSD license. As an example, any software which uses both OpenSSL (which inherited an advertising clause from SSLeay) and GPLed software is illegal. It seems silly, but it's a fact. By combining the two, you are violating the GPL, and thus the copyright of whoever owns the GPLed portion of the software. The exception to this is if the person(s) who wrote the GPLed section add a special disclaimer, since, as they are the copyright owners, they can do whatever they want. But anyone who wants to use OpenSSL and, say, readline in their application is out of luck (unless you can get an exemption from the FSF - good luck). Some people see the GPL incompatability as a feature, not a bug. In 1999 this condition was removed from the license by Berkeley, though this only affects software that was copyrighted by the Regents of the University of California (the restriction remains in effect for software written elsewhere). BSD licenses without this restriction are sometimes called "revised" BSD licenses.
The usual versions of the BSD license also require that anyone who redistributes the software may not use the name or affiliations of the author in advertising; saying "Our package foo uses special sauce developed by Bill Joy!" violates the license, unless you get Bill Joy, or whoever, to say that doing so is OK.
There are several close variations of the BSD license, including the gzip/libpng license (which has an extra clause forbidding misrepresentation of the software's origin), and the MIT/X license.
The text of the original BSD license is as follows. Some people give their copyright to the UC Regents (this is most common in the *BSD camps) while others replace the text refering to UC-Berkeley with their own names (or a project name).
Copyright (c) <years>
The Regents of the University of California. All rights reserved.
Redistribution and use in source and binary forms, with or without modification,
are permitted provided that the following conditions are met:
1. Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
this list of conditions and the following disclaimer in the documentation
and/or other materials provided with the distribution.
3. All advertising materials mentioning features or use of this software must
display the following acknowledgement:
This product includes software developed by the University of
California, Berkeley and its contributors.
4. Neither the name of the University nor the names of its contributors may be
used to endorse or promote products derived from this software without
specific prior written permission.
THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND ANY
EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR ANY
DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
† I'm not making a comparison between hate speech and commercial software here, it's just the best "you're free to do X, even if X is bad or evil" example I can come up with.