By my understanding, it is a sort of nervous system. Something very similar to one's heart producing blood and its path through the body. Although Tatsumi produces very little, it can be quite the problem at times.

[Mostly in that Berserker could very well kill him by using too much, which would be easy to do with his Noble Phantasm...]

Food can account for some, in just the way it would for a normal human. It is transferred to me through our pact. We share a sort of spiritual link. ...Well, not anymore, but we did, before this place. There are other ways to transfer prana, but- well, none I wish even to speak of.