8x8x8 multiplexed LED cube with an Arduino Mega 2560

Un4Seen:
But you also wrote "Then you latch and that row gets committed". What does it mean to latch?

When you bring CS (chip select) high the data is latched. That is, it is transferred from internal holding registers to the actual chip outputs, connected to the LEDs. Until it is latched you don't see it, so you don't notice the data being pushed from one chip to the next one, it is all internal.