FFmpeg is licensed under the GNU Lesser General Public License (LGPL) version 2.1 or later. However, FFmpeg incorporates several optional parts and optimizations that are covered by the GNU General Public License (GPL) version 2 or later. If those parts get used the GPL applies to all of FFmpeg.
Read the license texts to learn how this affects programs built on top of FFmpeg or reusing FFmpeg. You may also wish to have a look at the GPL FAQ.