I see this notation used in Linear and Quasilinear Equations of Parabolic Type, but it is not explained in the notation table
Moreover, it defines osc as the difference between the two.
I am guessing it means something like supremum or essential supremum but I am not 100% sure so I want to check this.
$\operatorname{vrai\, max} u$ denotes the essential supremum of $u$, the notation uses the French word vrai (true, essential) instead of the English essential. See for example in Yosida's Functional Analysis, p. 34.