An official lyric video is a label-released video that puts a song's written words on screen over a simple visual treatment. The background is usually static or lightly animated rather than filmed. The word official matters here. Fan-made lyric videos have existed for as long as the format has, but the official one is the label's own upload, which is why it usually sits on the artist's channel and carries the release links.
How does it differ from a music video? A music video is filmed content built to be watched, while a lyric video exists to carry the words. A label may release both for the same song, sometimes on different days. The other neighbor is the visualizer, which is a looping or abstract image with no words on screen. That gives us one simple test: if you see the words, it is a lyric video, and if you see only a moving image, it is a visualizer.
Why do labels release them? A lyric video gives a track its own video presence and its own page without the cost and schedule of filming. That is why non-title tracks and digital releases often get one, including tracks that do not get a music video. For a label, it is a practical way to give a song a home of its own on the channel without setting up a shoot.
For you as a fan, it is the version where you can follow the words at the pace of the song. When a song is in a language you do not read, it is often the upload that carries an official subtitle track, which you can turn on in the player settings. One practical note: the words shown are the official ones, so when fan transcriptions circulate that disagree, the lyric video is the version that came from the people who released the song.