Angular displacement

What is the problem of angular displacement at interpolation? I have heard this, but I cannot find nowhere a clear explanation.
What is the problem of an interpolation velocity with the linear angular interpolation?
Why do people use quaternion technique?

Look at a globe latitude and longitude.
Separately linear in each axis (latitude and longitude), however you see that the divisions are not equal, especially near the poles : that means that linear interpolation between any lat1,lon1 and lat2,lon2 is not trivial to do. Doing that in the quaternion space is much easier.