Original: The ray-finned fishes are so called because they possess lepidotrichia or "fin rays", their fins being webs of skin supported by bony or horny spines ("rays"), as opposed to the fleshy, lobed fins that characterize the class Sarcopterygii.
Simplified: The ray-finned fishes get their name from the fact that they have lepidotrichia or "fin rays". Their fins are webs of skin held by bony or horny spines ("rays").