The main reason people convert YouTube videos to MP3s is because it allows them to save the audio component of the video for offline playback.
This is useful, for example if you want to listen to a video podcast, an interview, a panel discussion, a TED talk, etc. while doing something else, like working or driving.
MP3 files are a lot smaller in size than video files, so if you don't care for the visual content, you can save up a lot of storage space on your device.
Also, a lot of people like to use MP3 converters to download the audio component of music videos to create their own song libraries without having to purchase individual tracks or pay for a subscription to a streaming service.