Open source licenses generally fall under two categories: Those that aim to preserve the openness of the software itself (copyleft licenses), and those that aim to give freedoms to the users of that software (permissive licenses).
An example of a copyleft free software license is the GNU General Public License (GPL). This license is aimed at giving the end-user permission to redistribute, reverse engineer, or otherwise modify the software under the terms of the license. These permissions are not entirely free of obligations for the end-user, however. The end-user must comply with certain terms if the end-user wishes to exercise these extra permissions granted by the GPL. For instance, any modifications made and redistributed by the end-user must include the source code for these, and the end-user is not allowed to re-assert the removed copyright back over their derivative work. The modified software is therefore also publicly available for further modification by any user.
Examples of permissive free software licenses are the BSD license and the MIT license, which essentially grant the end-user permission to do anything they wish with the source code in question, including the right to take the code and use it as part of closed-source software or software released under a proprietary software license.