LGPLv3 is the current version of the GNU Lesser General Public License. LGPLv2.1 is an older version and not recommended by the Free Software Foundation for new projects anymore. Both licenses have the same intention, namely to protect the freedom of users to use and modify the software licensed under LGPL.
LGPLv3 makes this intention very explicit. You have to provide means to the end user to install a modified version of the library licensed under LGPLv3 and run your software using that modified library. In practice, this for example refers to:
- Tivoization – Explicitly not allowing creation of closed devices where the end user does not have the LGPL granted rights for the Qt open source libraries
- DRM and hardware encryption – This cannot be used to circumvent these obligations
- Software patent retaliation – Where all users of the software are granted licenses thus making software patent retaliation of any potentially patented software in the distributed software meaningless.
