Most files in FFmpeg are under the GNU Lesser General Public License version 2.1 or later (LGPL v2.1+). Read the file COPYING.LGPLv2.1 for details. Some other files have MIT/X11/BSD-style licenses. In combination the LGPL v2.1+ applies to FFmpeg.
Some optional parts of FFmpeg are licensed under the GNU General Public License version 2 or later (GPL v2+). See the file COPYING.GPLv2 for details. None of these parts are used by default, you have to explicitly pass --enable-gpl to configure to activate them. In this case, FFmpeg's license changes to GPL v2+.
Specifically, the GPL parts of FFmpeg are:
Should you, for whatever reason, prefer to use version 3 of the (L)GPL, then the configure parameter --enable-version3 will activate this licensing option for you. Read the file COPYING.LGPLv3 or, if you have enabled GPL parts, COPYING.GPLv3 to learn the exact legal terms that apply in this case.
There are a handful of files under other licensing terms, namely:
FFmpeg can be combined with a number of external libraries, which sometimes affect the licensing of binaries resulting from the combination.
The following libraries are under GPL: - frei0r - libcdio - libutvideo - libvidstab - libx264 - libx265 - libxavs - libxvid When combining them with FFmpeg, FFmpeg needs to be licensed as GPL as well by passing --enable-gpl to configure.
The OpenCORE and VisualOn libraries are under the Apache License 2.0. That license is incompatible with the LGPL v2.1 and the GPL v2, but not with version 3 of those licenses. So to combine these libraries with FFmpeg, the license version needs to be upgraded by passing --enable-version3 to configure.
The Fraunhofer AAC library, FAAC and aacplus are under licenses which are incompatible with the GPLv2 and v3. We do not know for certain if their licenses are compatible with the LGPL. If you wish to enable these libraries, pass --enable-nonfree to configure. But note that if you enable any of these libraries the resulting binary will be under a complex license mix that is more restrictive than the LGPL and that may result in additional obligations. It is possible that these restrictions cause the resulting binary to be unredistributeable.