Primal is the equivalent of experience points on the original God Wars, and represents the Primal Energy you have absorbed from external sources. Imbued characters earn Primal for various activities (such as killing opponents) and can then spend it to improve their Age or Powers. An Unimbued character is not able to earn Primal.
Note that your Primal cap is (Age*Age)/5 - i.e., 2000 points at Age 100, 8000 points at Age 200, 18000 at Age 300, and so on. This number is also exactly twice the cost for training a stat. Your primal can go above this cap, but if you kill something after you have already reached or exceeded the Primal cap, your Primal will not go any higher - you will earn nothing for that kill.
It is also possible to earn ‘Safe Primal’, which doesn’t count towards your Primal cap, and isn’t lost if you are killed. Your Safe Primal is spent in exactly the same way as regular Primal, but is always used up first. It is generally earned from exploration and completing tasks.