The cubic yard is a unit of volume derived from the imperial system of units. It uses the symbol yd³.
It equals the volume of a cube with edges that each measure 1 yard. It is equivalent to 27 ft³, 46656 in³ or ≈ 0.764554 m³.
The yard (and derivatives like the cubic yard for example) are the same in both the imperial systems and US customary systems so require less conversion systems to calculate / convert to SI or metric.
The acre-foot is a unit of volume in the US customary unit system with the symbol ac⋅ft.
It represents the volume contained in a box measuring 660 feet long, 66 feet wide and 1 foot deep. This can be thought of a box the size of an acre but 1 foot deep.
It is approximately the same volume as an 8 lane swimming pool; 25 metres in length, 3 metres deep and 16 metres wide (assuming lanes are 2 metres wide).
It is still used in the US despite its links to the much-outdated imperial system of units. For example a "rule of thumb" is that an average suburban family's annual water usage should be around 1 acre-foot. This is equal to just under 3.4 m³ daily.