From the Super Mario Wiki
The Owl is a character from Donkey Kong 64 that lives in the big tree in Fungi Forest. As would be expected with an owl, he can only be encountered at night. Apparently he won't talk to anything that can't fly, as he told Diddy Kong before he got his Rocketbarrel Boost. After Diddy got the rocketbarrels, the Owl, in similar vein to the Necky in Angry Aztec, challenged Diddy to get through his obstacle course by flying through rings he leaves behind. After Diddy beat the course, the Owl was disappointed to find that his obstacle course was not as hard as he thought it was. The Owl then rewarded Diddy with a Bonus Barrel.