The purpose of the Rune command is to allow you to use healing spells outside of battle, as well as to let you see how many charges you have left of that spell. Greyed out spells such as Deadly Fingertips basically mean that they're in battle only (or you're out of charges). Unfortunately the game doesn't do a very good job of telling you what each spell or command does, but I do recall spells having in battle descriptions that'll help give you an idea on what they can do. At the very least many runes and spells are fairly obvious in their function (Fire Rune casts fire magic, Soul Eater has a number of instant death attacks, Water uses healing magic, ect...).
To help you along here's some pointers:
Runes with element sounding names like Fire, Water, Lightning, ect.... are spell runes. Give these to characters with high magic scores aka casters or supporting characters who aren't really good at attacking.
Runes with animal sounding names like Boar and others are attack runes. They typically have only one function that lets its user use a special attack. Fighters tend to have these and some are character exclusive (but not all, like the Boar rune).
Runes with odd sounding names either fall into two separate categories; special effect runes or special attack runes. Runes like Holy and Sunbeam have special effects (allows you to dash and heals its bearer respectfully) whereas runes like Clone and Trick are also special attacks like the Boar rune. These can typically go on whomever though those who come with them should probably keep them.
And then there's one other set of runes that are basically high powered versions of the standard spell runes that magic users basically have dibs on since they offer a new fourth level spell in place of the old first level spell (effectively giving you access to spell levels 2-5 instead of levels 1-4).
Embedding adds effects to your character without taking up that character's rune slot. Standard elemental ones add an effective element to your weapon. Fortunately weapon elements only consider if the enemy is weak to that particular element and do not reduce a character's damage output if they attack an enemy that resists that particular element. This however does not apply to elemental spells as there are many enemies that can mitigate or nullify elemental spell damage. They can also add additional effects like Water runes healing your character for a small amount at the start of every turn or Fire runes adding an additional fire attack following your attack (which can be resisted), additionally you can stack up to nine runes onto one weapon as long as they are the same type to increase the effect of the supplemental effect (more Water runes increases the amount you heal by per turn, more Fire runes increase the amount of damage the additional fire attack does, ect...). However once you embed a rune onto a weapon it's gone for good although you can embed a separate rune onto a weapon with a rune already embedded onto it to overwrite the old rune so you don't have to worry too much about screwing yourself over.
And finally, rune pieces that with attribute names like Magic, Skill, Luck, ect.... are used like consumables that'll add a point to a character's respective stat. I think elemental rune pieces also fall into this category which is why you can't attach them to your weapons, but it has been a while since I last played this game and this is all off the top of my head.
Anyways, hope this helps.