As of patch 1.23 (August 2017) powersurge has been removed as a specific skill. The three cards that previously had Powersurge have been reworked and now have a Summon skill of "Spend your remaining power to...". The main motivation for this change apears to be to clarify the interaction with cards like Eilyn's Choice that depend on the power cost of a spell.
The information belowis for archive purposes.
"When played, spends all of your remaining power to increase its effect."
Cards with Powersurge are indicated with an X in the top left corner instead of a power cost. As of card set 1 there are only three cards with this skill: Charchain Flail and Flame Blast for the Fire faction and Copper Conduit for Justice.
What Does Powersurge Mean?
Most cards in the game have a fixed power cost to play, indicated at the top left of the card. Powersurge removes that cost: so long as you have the right influence you can play it at any power level. However the more power you have the more effective it is.
How does that work? Well, when you play the card it uses up all your remaining power that turn. How that power is spent varies between cards and is specified in the card text. Note that it's your remaining power not your maximum power. So if you have 10 max power, play units for a cost of 7 then play a Powersurge card, the Powersurge will only be 3 strong.
Smart use of Powersurge is all about timing. The longer you can go without playing, the more useful it is - but don't wait so long that you miss your chance!
In addition Powersurge usually works best with a deck based around gaining high levels of power rather than one based around lots of spells or cheap units.
All of which makes the inclusion of Powersurge cards in the Fire faction seem rather strange to me - I don't see it a good fit. However they can work as a useful finisher if a game goes on past the early stages.
This page written for Eternal version 1.23, Card Sets 1 & 2
Last updated: 16-08-2017