Maybe more than a paragraph but from a cursory read looks like it might give you what you want. Wikipedia (free online encyclopedia contributed to by web users) has articles:
http://en.wikipedia.org/wiki/OpenSource
http://en.wikipedia.org/wiki/Linux
Note that Linux is an open source operating system but not all open source is Linux so you should be careful to denote what your interest is. If you want to discuss Linux primarily then a short definition of open source would be appropriate but you shouldn't dwell on it.
Essentially Linux is the operating system. There are multiple open source applications that can be loaded on it (or on other operating systems). Some applications are available for Linux and other operating systems (including Unix and Windows) for example Perl which is a scripting/programming language. Since they are "open source" anyone with good knowledge of the language they are written in (primarily C for Linux/UNIX open source stuff) could compile them for operating systems such as Windows which itself is NOT open source.
More briefly I'd say:
Open Source is source code that is free to use and compile as needed that can not be modified or sold based on most licenses (mainly the GNU Public License a/k/a the GPL).
Linux is an open source operating system clone of UNIX.
Note there are multiple Linux distributions and different versions with in the distributions. Most are freely distributable and installable but have no direct support from any vendor. There are distributions (Notably RedHat Enterprise Leve a/k/a RHEL, and Suse Linux Enterprise a/k/a SLED) for which one can buy support from the making vendor.
