Term used in Nicolas Bourbaki's Élements de Mathématique to describe a set taken along with a binary operation on that set. Closure with respect to the operation is, of course, assumed. Semigroups, monoids, groups, etc. are all special cases of magmas.
Nowadays, most people use the term `groupoid'. That term, however, can also refer to so-called `virtual groups', which have much more structure than magmas.
In non-mathematical French, magma means (in addition to molten rock) `jumble' or `random conglomeration'.