Agile Product Development: What’s your MVP?

MVPs are often used as a way to chunk up our full feature scope into manageable parts that we can implement one step at a time.
This approach does not really help us in much in deciding what should be in scope or out of scope, and what should be high priority or low priority.
The true power of MVPs is facilitating fast learning.
Will our proposed solution actually bring the business impact and value we think it will?
What assumptions need to be true to achieve this impact?