Always check the definitions being used in the reference - there are even slight differences between HAG2 and Toen's global overview. Once you know you have an epimorphism from a union of affines, saying that $X$ is $n$-geometric in the HAG2 sense basically amounts to saying that the higher diagonal 
$$
X \to \mathrm{map}(S^{n},X)
$$
is affine. Thus $0$-geometric is equivalent to semi-separated, and any algebraic space $X$ is $1$-geometric because $\mathrm{map}(S^1,X)\cong X$.

EDIT: in response to keaton's comment, the condition isn't quite equivalent to $n$-geometricity, as there are some epimorphism conditions to check, but arises inductively because 
$$
X\times^h_{\mathrm{map}(S^{n},X)}X \cong \mathrm{map}(S^{n+1},X).
$$