Refers to the act of leaping or springing, often with a sense of vigor or excitement. The gloss 'exciting' is a derived nuance, not a standalone meaning.
The fish leaped out of the water.
His heart was full of excitement.
躍り (leaping, springing) and 踊り (dancing) are pronounced identically but refer to completely different actions, so they are easy to mix up when written or heard.
Used for 躍り (dance/leap) when counting occurrences of the action, as in 「1回の躍り」.
The nominalized form of the verb 躍る (おどる, 'to leap, to jump'). The kanji 躍 carries the meaning of 'leap' or 'spring'.