Tsaheylu is a Na'vi word meaning a bond (neural connection). This bond takes place when two creatures of Pandora connect their queues. Some instances where this bond would occur are those between a Na'vi and a direhorse, or a Na'vi and a mountain banshee. However, the bond can also occur between the Na'vi and other creatures like the thanator or the great leonopteryx. Almost every creature on Pandora has a queue used for tsaheylu, although some don't have any that are noticeable.
The Na'vi connect their queues during mating to create a strong, emotional, and lifelong bond. Now think about that. The same thing they use to form strong bonds during mating, is also used with animals. Oookay, man. Whatever floats your alien boat.