metric system is so much easier: m³
Just like with board feet it doesn't say anything about the actual dimensions. Also, I don't think it's much better as a unit than board feet either, both have very unclear relationship to the actual amounts you need. You'll always need to do a pretty complex calculation to figure out how much you'd need to buy. The pricing is mostly useful as a comparison to look at relative or day to day pricing differences.
A board foot is a measure of volume - with an implicit third dimension.
So you could just use the SI unit for volume.
A board foot ~= 2.4 litres.
This seems a bit silly though, as timber is not fungible in the way you'd expect a volume of something to be.
As noted by sibling comments, you very much can buy timber in cubic metres - a convenience for costing / transport - but you're not going to buy timber without knowing dimensions of the individual lengths.