The fire of love "serpe" (snakes) in the knights' hearts: a verb much beloved by Tasso, here suggesting a temptation like the one carried out by the Serpent in Eden. Armida, in fact, corresponds to Lilith, the non-human demon with a woman's face, as it can be seen in so many Medieval and Renaissance - and later - paintings on the original sin.
And the fire of love "s'apprende," clings to the knights' hearts. This is a literal quotation from Dante, Inferno 5: 100 ("doth . . . seize" in Longfellow's translation), where Francesca Da Rimini tells her tragic love story, that made her wind up in hell. So, it would sound like an alarm bell in the knights' ears -- if only they could hear it.
By virtue of Armida, the god Eros "surpasses himself." Here a reference can be seen to Dante, Purgatorio 31: 83 (though in this case the wording is not exactly the same), where the enchanting woman is no less than Beatrix. So, Armida really tries her best; and not by chance, this verse of Dante occurs in an episode set in the forest on top of the mountain of purgatory, that is precisely Paradise.