From the Domain & Settlement Selection FAQ (found in the bottom right corner of the page):
Q. What is Self-Sustainability and what can I do about it if it's low?!
A. Self-Sustainability measures the ability of a settlement to support its population using only the resources and facilities it already has access to. Rather than being an indication of how viable a settlement is, it is an indication of how independent that settlement is. A settlement with low self-sustainability must rely on outside trade to support its population. In Exposition and beyond, the self-sustainability of a settlement can be improved by employing better strategies for growing or raising food, improving infrastructure to allow more of each parcel to be dedicated to food production, or employing new technologies to make better use of the food the settlement already produces. It's also possible to simply forge relationships with neighboring settlements and trade, creating a stockpile of foodstuffs. This can increase self-sustainability for as long as the stockpile lasts.
Q. What happens if I don't address low self-sustainability?
A. In the absence of an external source of sustenance, such as trade with a neighbor, a below average self-sustainability will mean that the citizens of your town will experience shortfalls in food or other life-sustaining goods. This will increase their desire to find new opportunities outside the settlement. As each citizen surpasses its comfort threshold, that citizen, and that citizen's family, will migrate to a new settlement where their needs can be met. This is not an instant process, as each citizen of Elyria has their own personality and their own comfort levels, but as each citizen leaves, their leaving could be taken as a sign by other citizens that it is time to move on, and a sort of "cascade failure" is possible, where a small trickle of emmigrants leaving your settlement becomes an exodus over time.