GPL vs LGPL vs non-free
GPL: Your source code needs to be open source. The license most prebuilt FFmpeg binaries ship under. Bundles x264 / x265 (most commonly used encoders) but forces distributing apps to be GPL too. Distributing new code built on top of GPL-licensed code requires the new code to be under GPL and the source code to be available. You are allowed to use the FFmpeg binaries as-is in your own application as long as you don't distribute the software. FFmpeg's legal page puts it plainly: "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."
LGPL: Your source code can be closed source. The license for FFmpeg's own libraries (libav*) — see the LGPL v2.1 text. Drops the common GPL plugins and encoders. You can bundle it into closed-source or commercial software without releasing your own source code. For full details see the "License Compliance Checklist" section in FFmpeg's legal page.
Non-free: These builds pull in libraries whose licenses are incompatible with the GPL and require a paid commercial license to distribute.
See FFmpeg's legal page for the canonical reference.
* The above is not legal advice — verify each license against your specific use case before distributing.