Lots of things are still defined per liter (such as molarity. How is that in imperial units anyway? pound-moles per gallon?) which doesn't make much sense either.
A litre[1] is a 10x10x10cm cube, (a cubic decimetre), which may seem a bit strange and non-SI (cubic metres would be more in line, one thousand times the volume), but a litre of water weighs (under normal Earth gravity) exactly 1kg, the SI unit of
weightmass[2]. This is no coincidence.
A cubic metre of water weighs (with the same caveat) a tonne, otherwise known as a megagramme, but it's also 'nicer' to have a handy-sized litre as opposed to something 1,000 times the volume but which would often used to measure household volumes of liquid where people appreciate a more simple order of number. Although I suppose they could have gone the same route as the kilogramme itself, which is the primary SI magnitude of mass rather than the non-prefixed gram (that being much too small for household quantities, save in the order of 100s (10s at a push for some things, unit numbers only rarely so) at a time).
[1] Or on your side of the pond, presumably: liter... but my spill-chucker rebels over that variant. As much as yours would mine, I suspect.
[2] Weight and mass being so synonymous, I momentarily made that error. Other similar ones may be found drizzled throughout my prose! YKWIM, though...