It is the class of functions that have the constant value 0, with a canonical exemplar f(n) = 0 (and despite having tried, I cannot find any other function, up to choice of variable name).

In terms of algorithms, I suspect that no actual algorithm fits into it and as such it is more a curiosity than actually useful.

However, O(0) is not the same as O(1), as we cannot find a constant c such that 0c dominates all possible functions that 1c can dominate.

No-op :)