Let $G$ be a complete reductive Lie group. A simple root $\alpha$ is said to be minuscule if the multiplicity of the coroot $\alpha^\vee$ in $\beta^\vee$ is at most $1$ for all positive roots $\beta$. Associated to a minuscule root $\alpha$ is a maximal parabolic subgroup $P_\alpha$ of $G$, and the quotient $X = G/P_\alpha$ is called a minuscule variety and has various nice properties (see the textbook of Billey and Lakshmibai for details).

In the case $G= SL_n$, all the simple roots are minuscule and the corresponding minuscule varieties are complex Grassmannians, which can be thought of as parameter spaces for $k$-dimensional linear subspaces of an $n$-dimensional complex vector space.

In the other classical types, we can also understand the minuscule varieties $X$ that arise as some sort of parameter space, where for example the points of $X$ correspond to subspaces that are isotropic with respect to some bilinear form.

That leaves exactly two minuscule varieties of exceptional type. One is the projective plane over the octonions, which is not too bad. The other comes from Lie type $E_7$ and I don't know how to interpret it as a parameter space. What is this space? Is there a way to describe it (even non-rigorously) that avoids Lie theory?

Sometimes the name Freudenthal is attached to this space, though I don't know that he studied it explicitly. I have also seen it given the notation $G_\omega(\mathbb{O}^3, \mathbb{O}^6)$, which is suggestive; unfortunately, I've never seen this notation explained anywhere, so I don't know how to interpret it.