Translation:The invention of electricity was important.
invent - εφευρίσκω
discover - ανακαλύπτω
You discover something that was always there, but "hidden". For example, you can discover a new planet, or you can discover how to make steel from iron.
You invent something that is new, that was only in your mind before. For example, many years ago, people invented the wheel. Later, people invented steam engines, cars, and computers.
why not "his invention..."?
That would be η εφεύρεσή του with two accents.
Also, η εφεύρεσή του ελεκτρισμός would not be grammatical.
"His discovery, electricity, ..." would be η εφεύρεσή του, ο ελεκτρισμός, ....
And 2nd, electricity was discovered, not invented.
That was already mentioned on this page; there's no need to do so again.