should i install ffmpeg in my fedora system by installing it will i get any better support if yes then in where and if not then what it use for.
You probably already have it installed.
It is used for encoding and decoding audio and video and many applications depend on it.
FFmpeg is used for example by mpv and yt-dlp, the latter being a YouTube and other videosites downloader, merging audio and video tracks together…
You can use it also to convert many video files into other formats, for example from mp4 to WebM or audio… Swiss Army knife!
And Firefox needs it for playing certain videos. You should then install ffmpeg from rpmfusion-free rather than ffmpeg-free from the fedora repository. The latter may not allow you to play certain videos.
Yes, you are right, get the version from the rpmfusion repositories!
Since the ffmpeg-free package installed by default by fedora is restricted as to the codecs it is able to use, most benefit will be achieved (and the most codecs available used) if you were to replace the version installed by fedora with the one installed from rpmfusion.
That is done by first enabling the rpmfusion repos as shown here then do
sudo dnf swap ffmpeg-free ffmpeg --allowerasing
Apparently the ffmpeg swap is not necessary? I just enabled the two RPM Fusion repos first and then installed FFmpeg with only this:
sudo dnf install -y ffmpeg