Compared to H.264/AVC, you can get the same level of video quality in ~half the bandwidth (or double your quality for the same bandwidth).
Compared to H.265/HEVC, AV1 has no patents and so anyone can implement it without worrying about licensing (there seem to 3+ groups that need to be paid off).
The trade-off is that it is more computation intensive than H.264 (as is H.265).
Quite a lot actually. This codec is much more efficient at producing high quality video recording / streaming at much lower than normal bit rates when comparing to x264/5. Epos Vox has a good video describing the benefits: https://youtu.be/sUyiqvNvXiQ
H.264's most likely successor was HEVC. While Google and Mozilla strongly prefer VP8/VP9, most video content distributors are okay with paying the license fee for H.264. One patent pool, one license fee. HEVC's patent pool fragmented. So even after you pay one fee there might be another one or even worse patent trolling litigation. So non-broadcast companies are adopting av1 to avoid using HEVC when possible.
Compared to H.265/HEVC, AV1 has no patents and so anyone can implement it without worrying about licensing (there seem to 3+ groups that need to be paid off).
The trade-off is that it is more computation intensive than H.264 (as is H.265).