Quaternions, in case you didn’t find a satisfying answer Googling, are a type of complex numbers that the mathematican Hamilton invented (sometime in the 19th century, if I’m correct). What differs these from “normal” complex numbers are that these consists of four parts (a 3D vector and a scalar) instead of two. In the same way that you can plot complex numbers on a 2D graph, you can plot quaternions in a 4D space. I’m quessing that the fourth parameter is used as time, but I’m not sure since I only program 2D apps and not 3D. It might also be ignored completely.
Anyways, traditional 3D animation (real-time that is, like in games) uses the same principle as RVKs (relative vertex keys) in Blender. They consists of keyframes (like stills in 2D animation) where vertices are translated to where they are supposed to be at that time. If the application wants to draw a pose of an 3D actor between two keyframe it renders an interpolation between the two frames.
So I guess what you would want to do (depending on how the targeted format is constructed, of course) is to find a way to export your keyframes to quaterion (or similar) matrixes, but I’m merely guessing since my real-time 3D knowledge is limited. I’ll leave it to the pros to fill in the blanks.