FFmpeg may be licensed either by GPL or LGPL depending on what is included in a compiled copy. Typically it is GPL. Check the FFmpeg documentation for what determines the choice of license.
There are a couple of pieces of text in the GPL license you need to look at...
Activities other than copying, distribution and modification are not
covered by this License
Since you are not copying, distributing or modifying FFmpeg, the license does not apply to you. This is probably also true of any person who is merely running your program (assuming that your program does not, for example, automatically install FFmpeg).
This License applies to ... "work based on the Program" means either the Program or any derivative
work under copyright law
A program which calls FFmpeg using the command-line is probably not a derivative work of FFmpeg, since it does not contain any portions of FFmpeg. So if you did copy or distribute FFmpeg in this case, you would need to follow the GPL requirements in regard to FFmpeg itself, but not in regard to your program or the combination of FFmpeg with your program. Your program can be covered by a separate license (eg commercial).
Note that if your program linked with a DLL instead of using the command-line, that probably would be a derivative work because (at least in C or C++) linking with a DLL requires including headers which potentially result in portions of the header code being incorporated into the host program. In that case the GPL requirements would apply to the derivative work as a whole.
Note that FFmpeg may contain a number of patented algorithms, for example MPEG-2, H.264 codec, etc. While you probably don't need to worry about it because you don't "manufacture, import, use, sell or offer for sale" the patented code (ie portions of FFmpeg), your users probably do have to worry about it. For example, H.264 patent licenses can be obtained from MPEG-LA. There are a number of exemptions in which an automatic free license is granted (and no registration is needed). However, many commercial uses (even if just in-house and not for-hire) are not exempt. License fees tend to be minimal, but dealing with the required paperwork can be a huge hassle - good luck!
I'm not a lawyer; this is not legal advice, just my personal opinion from reading the license. I have dealt with GPL and MPEG licensing a number of times in a commercial context.