Normally a player runs the side as a whole, and all the units on that side are disposable and interchangeable. However, you require one unit to represent the player personally among the units of the player's side; this unit is the self-unit. What this means is that if that unit is captured or dies, the player loses the game instantly. All the other units on the side will behave normally as for losing, either going over to the side that captured the player, becoming independent, or disbanding.
The idea is to increase the player's motivation for self-preservation. This is useful to introduce a risk of capture, assassination, and so forth. It also prevents bizarre and unrealistic strategies in some games.
For instance, it sometimes happens in empire-building games that players end up switching countries, because each captured another's country and neglected to defend their own. If each player got one capital city, and that city were to be a self-unit, then the owner would have to defend it at all costs!
To make this happen, you could do something like this:
(set self-unit-required true) (add capital-city can-be-self true) (add capital-city start-with 1)