Board Game Arena

I can't find a suitable explanation in the rules linked here.

Boost is a bonus effect on some abilities that's only active if something else specifically gives it boost. No generic way to gain it.
There's various ways to activate boost in other expansions but for Massive-Verse it's just Pyre's passive.

Any of Pyre's abilities will always do their regular effect. If you used his passive that turn they also get the boost effect.

Side note for Legacy: you can pass his abilities to other characters but since none of them can activate boost they'll only get the regular text.