An ultra masculine way of saying "I".
Momotaros from Kamen Rider Den-O uses "ore" when referring to himself. He's the perfect character to exemplify this because of his cocky, arrogant, testosterone-driven attitude. It's also a part of his catchphrase "Ore sanjou" which means "I appear!"
Describing a person as having an "ore personality (ore seikaku)" would be to say that person is extremely egotistical or arrogant.
Beet J Stag from Tokumei Sentai Go-Busters has an extreme ore personality. He literally tells people that he is only interested in himself. Plus almost all his lines include Ore in them, thus making everything about himself. An example of his unnecessary use of ore is when he says "Activating my Marker System" instead of saying "Activating the Marker System".