What is the role of morphisms $A \rightarrow \mathbb{Z}$ in algebraic geometry?

Question

From Steve Awodey's Category Theory, p. 37:

Ring homomorphisms $A \rightarrow \mathbb{Z}$ into the initial ring $\mathbb{Z}$ play an equally important role in algebraic geometry.

My question is thus, for someone who knows a reasonable amount of abstract algebra but zero algebraic geometry, what exactly is the role of such morphisms in algebraic geometry?

Answer 1

These correspond to scheme maps $\text{Spec}\,\Bbb Z\to\text{Spec}\,A$, so to points of $\text{Spec}\,A$ defined over $\Bbb Z$.