Manpower is used to defend planets from invasion, and man ship crews (and now, boarding actions against ships - which is hilariously overpowered). Ships without enough manpower have a penalty - I think it scales linearly to a 20% damage debuff with no crew at all. (Maybe it’s better to think of it as a 20% buff for having full manpower!). Ship manpower is also used to invade planets.
Manpower is created from food - by default, 10% of food production is converted to manpower. Some buildings can increase this ratio (Patriot Pills and another I forget). You can also get it from trade or treaties with minor races.
Don’t worry too much if you are running out. Just be aware that your planets will be vulnerable to ground invasions until their garrisons are stocked, and your ships won’t be at peak efficiency. Unless you’re going to war soon, you can ignore it.