Old container, often perfectly good contents
AVI files mostly come from a specific era: camcorders, early digital cameras and the DivX/XviD encoding scene of the 2000s. The container has aged badly, but the video inside frequently has not. MPEG-4 Part 2 video, which is what DivX and XviD produce, is something today's MP4 can hold natively, and MP3 audio slots in just as well.
That is the quiet trick of this page. Instead of re-encoding twenty-year-old footage and stacking new compression artifacts onto old ones, the tool inspects the file and, whenever possible, simply moves the streams into a modern MP4. The picture stays exactly as it was, and the conversion runs at read speed.
When re-encoding is unavoidable
Some AVIs hold formats from even further back, like Cinepak, Indeo or raw DV. MP4 has no place for these, so the tool re-encodes them to H.264 with AAC audio. It decides this per file, before starting, and labels the row so you know which kind of job you got. Browser re-encoding is slower than real time; for one family-archive file it is fine, for a whole box of tapes a desktop tool will serve you better.
One more honest note: a remux keeps the original codec, and a few very old smart TVs only decode H.264. If your copied MP4 still refuses to play somewhere, that is why, and the video converter page re-encodes it properly.
What comes out
An .mp4 with the same picture whenever the copy path applied, a front-loaded index so playback starts immediately, and your original filename with the new extension. Files up to 500 MB are accepted, batches queue one after another, and nothing leaves your browser at any point, which is exactly the right property for digitised home movies that exist nowhere else.