Waw primarily joins, but in some contexts it has a figurative circumstantial (hal) use. The following clause is then understood in a relation tied to the preceding act.
«أد إلي ألفا وأنت حر»
Pay me a thousand, and you are free.
In the textbook’s historical manumission illustration, payment is understood as a condition of freedom. The particle is not merely combining two independent statements: the context gives them a conditional relationship.