Placing two Runes of the same type next to each other will give you a stronger version of the spell/skill. Shield rune is a bit special though since putting an elemental rune next to it will give you *Element* Shell which is a buff spell that gives you resistance to that element.
Two 'Fang's will give you Double Fang for instance. Two 'Cure's would give you Restore. Two 'Spray' runes give you Water. If you're lucky with treasure contents or save scum, you can get some of the "level two" runes like Water which is honestly better than using two "basic" runes to get them since you save a slot for something else.
There are also runes that boost your max HP/MP or a stat.
There are status effect spell runes as well of course.
Also, you can buy more rune slots by paying AP in the learn skills section of the menu.