There are several open source licenses in use. The most widely known is probably GPL, the Gnu Public License, created by Richard M. Stallman. A variant is the Lesser Gnu Public License, or LGPL.
Other open source licenses include the BSD license and the Mozilla Public License.
Open source licenses cover copyrighted code. You are allowed to get the source and make changes, but you are generally expected to contribute your changes back to the original authors or current maintainers to benefit other users. You are also allowed to distribute your changes, as long as you maintain the original license and credits, and do not try to pass the result off as your own work. If you wish to make a "closed source" version of the program where you do not make the source available, you must negotiate a closed source license with the owners of the code.
Most open source code is also available free of charge, but the licenses do not require it. It is possible to charge for products released under an open source license, and some developers do.