Matthew Hayward, I think I understand now. 🤞
When you use Boost, you channel the magical energy from what
would (could?) have been a spell you cast into the physical attack of an ally. Though you're not technically casting a spell, the spell consumed by Boost gets marked off your class card.
Here's a specific example (you're an elf wizard, I'm a dwarf fighter):
We're fighting the
BBEG
. During the course of our adventure, you've noticed I'm really good at sliding--I almost always land on the 20. It's getting down to the wire. Your only remaining offensive spell is Fireball. You're down to 9 HP, so you can't use MEC. The BBEG isn't extra-vulnerable to Fire, so the most damage a Fireball could do is 20. But since you know I'm almost certain to crit this SoB (dwarf fighters deal triple damage when they crit on a natural 20), you use Boost to channel what would have been your Fireball spell into my swing. Fireball gets marked off your card, you take 5 damage, but no magical fire is created. Instead, the raw arcane energy that would have otherwise been converted into Fire gets shunted into the kinetic energy of my swing. Just to sweeten the deal, you use your Standard Action to cast Bull's Strength on me. I make a roundhouse at the BBEG with my
Enormous Hammer of Definitely Not Compensating For Anything and squash it like a bug under a steel boot. I'm covered in gore and we emerge from the battle victorious. Later on in the tavern, I buy you your beverage of choice for being such an awesome team player.
In a variation of the above scenario, instead of casting Bull's Strength on me, you could have used your Standard Action [using an (Arch-)Mage Power requires a Free Action] to drink a healing potion, make a physical attack, or pretty much any other Standard Action.
Though it wasn't part of the scenario above, Boost is particularly useful if you're within an anti-magic zone because it is not negated by the anti-magic effect.
Does that answer your questions? If not, tell me what I didn't cover.