When people are nearing death, they can make a complete copy of their brain (down to every last neuron) within the confines of the artificial one. It doesn't transfer their consciousness as such - but creates a
new copy, which has all the memories, thoughts and feelings of the old one. That person then goes off to die, whilst the 'new' version of them lives on - perhaps infinitely. And from the perspective of the new one, it believes it is the original - perhaps in a different form, but it has every memory and all the same characteristics and such.
I've a feeling that the virtual Jor-El AI may be similar to this. The original Jor-El will die on Krypton, but before he does he may create a copy of his mind, for want of a better expression. Rather than hosting it in a new physical body however, it will materialise as a hologram. And by having all the traits of his original mind, it will be able to answer anything that Jor-El knows (up until the point he copied his mind, at which point this new version began carving its own future) and will also retain all his thoughts, feelings and emotions towards his son.
On Earth, we take videos, photos and blogs to keep a history of our lives. Kryptonians are significantly more advanced than us (25,000 years of space travel behind them) so their method of recording their history may be a lot more complex
