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It is still used in the US despite its links to the much-outdated imperial system of units.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.
The barrel is a unit of volume used in the oil industry with the symbol bbl.
Oil is more commonly expressed in terms of cubic metres (m³) but in the US and in the economic world (mainly because such a large percentage of the world's oil is shipped to the US) as barrels.
The measurement of the barrel originated in the US at the first oil well in Pennsylvania. There were so many variants of barrel size (including those used for wine and other goods) that the distrust became so prevalent a central and standard barrel size was created. This was finally established in 1872 as 42 US gallons.