How do Melobloom's crit thorns work?

The thorns only fire on a critical hit from a Grass Aniimo, so a team with a non-Grass damage dealer gets nothing from them. The buff does no damage on its own. It turns the crits your Grass attackers are already landing into a second hit from the ground.

That makes Melobloom a support whose value scales with the team around it. In a Grass lineup the hits come from attackers such as Thornblade, the usual main DPS, or Irisalis, and the more often they crit, the more thorns you see. Melobloom itself is mainly there to support, not to deal damage.

Melobloom's ultimate, Rose Garden, gives allies inside its circle a 70% increase to Grass critical damage for 30 seconds. Thorns appear on crits, and Rose Garden makes those crits hit harder, so the two are designed to overlap. Keep your damage dealers inside the circle while the ultimate is active.

What else critical hits trigger

Crits do a second job for Melobloom. Once a target has taken three critical hits, its rose mark blooms and heals every ally nearby for 5% of Melobloom's HP. A crit-heavy Grass team therefore gets regular small heals as well as the thorn damage, and Melobloom also cleanses debuffs and negative status effects from the whole team.

You only have access to any of this after evolving Budsquire into Melobloom, which requires finishing the Flowers and Thorns journey quest.

Not settled: Grass teams are relatively weak right now and are expected to get stronger once Iris Solace becomes available. How much the thorns contribute depends on how much your Grass attackers crit, so their value may change when that happens.