H.264
H.264 was finalized in 2003 and has dominated web video ever since. It uses a combination of motion prediction (only storing the differences between similar frames), spatial transforms, and entropy coding to achieve compression ratios around 50:1 — meaning a 1-hour 1080p video that would be 670GB uncompressed compresses down to roughly 13GB or less depending on quality settings.
The reason H.264 dominates over newer codecs (H.265 / HEVC, AV1, VP9) is hardware support. Every iPhone, Android device, smart TV, web browser, and gaming console has H.264 decoding built into the GPU, so playback is essentially free in terms of battery and CPU. Newer codecs offer better compression but require either software decoding (slower, drains battery) or newer hardware that not all users have.
When you download a video from a social platform, the file is almost always H.264 video inside an MP4 container with AAC audio. This combination is the de-facto standard for shareable web video and plays on every device you'd ever want to play it on.