Ignitions are special, more powerful boosts. You buy them in the shop for black orbs, at !shop list ignitions, but they won't be too cheap. Once you buy them you'll notice that you can't use them immediately because they require a certain amount of your Ignition Gauge to use. You buy points into your Ignition Gauge capacity via the shop (also not too cheap when compared to the other attributes you can buy). You'll notice that your IG is not filled when you buy into the maximum. In order to fill the IG you have to be in winning battles or be killed by monsters.
Once you have enough IG to use the Ignition, you activate it the same way as you would a weapon boost: /me goes name.
You'll notice that Ignitions have two special extras in addition to attribute gains: augments and effects. Augments work just like weapon augments, but they're only temporary until the Ignition is turned off. The Ignition effects are immediate and activated when you first use the Ignition. The effects will either affect yourself, your allies, or your enemies by usually inflicting a status effect. You can manually stop the Ignition before running out of IG by using the command /me reverts from name on your turn. Any effects that are activated when you use the Ignition are not lost when you revert manually (unless it's a one-turn type effect that would normally be over upon the target's turn anyway).