Firstly, that sphere that you've pictured is convenient for thinking about what's going on, but remember that it is not what is actually happening. So the fact that you don't visualise light as having a little arrow pointing somewhere doesn't matter.
The fact of that matter is that for an electron spin, having the two possible states "up" and "down", we associate two distinguishable states, which we label as perhaps $|up\rangle,|down\rangle$ or $|0\rangle,|1\rangle$. Since quantum mechanics is a linear theory, and linear superposition of the two is allowed, $\alpha|0\rangle+\beta|1\rangle$.
Similarly for a photon, there are two distinguishable states of polarisations, horizontal and vertical. You can label these as $|H\rangle,|V\rangle$ or $|0\rangle,|1\rangle$. The labels really are arbitrary. But again, because quantum mechanics is linear, you can have a linear superposition of these, $\alpha|0\rangle+\beta|1\rangle$, and you can capture the same information as you can with the state of an electron.
On the Bloch Sphere, particular points are often highlighted, such as $0\rangle$, $|+\rangle=(|0\rangle+|1\rangle)/\sqrt{2}$ and $(|0\rangle+i|1\rangle)/\sqrt{2}$. If we've decided that $|0\rangle$ is the same as a horizontally polarised photon, then $|+\rangle$ is the same as a photon polarised at $45^{\circ}$, and $(|0\rangle+i|1\rangle)/\sqrt{2}$ is the same as a circularly polarised photon.