Let's say there's a disc on a table that rotates at 60 rpm. When you are standing >still it spins at 60 rpm. But if you start running around it, it will move faster >or slower relative to you. In this case, the disc has a ground speed, 60 rpm, >because it has something to spin in relation to, in this case, the table.
The spinning black hole is a solution of the vacuum <PERSON> equation that describes the spacetime interval $ds^{2}$ which is an intrinsic property of the spacetime itself on which all the observers agree. In other words, what we call a spinning black hole is the spacetime itself, so the example described by the rotating disk on the table is not a good analogy.
Now, let's say that there is a spinning black hole. Because there is no control >for the black hole to spin relative to, its spin must be relative to an object, >for example, you. 562
If you stand still, it spins at a constant rate. But if you >start moving around the black hole in the same direction as the rotation, >according to Newtonian physics, the black hole would spin at a slower rate >relative to you. Since a faster spinning black hole has a smaller event horizon, >in the first case, there would be a smaller event horizon.
Then how do scientists say that there are spinning and non-spinning black holes? >Is that just in relation to Earth?
The meaning of the spin is that any observer outside the black hole and sufficiently close (i.e. in the ergosphere) can not stand still. This is called the frame-dragging. The "least rotating observer" is a locally non rotating observer whose angular velocity, defined by an inertial observer at infinity is $$\Omega = \frac{d\phi}{dt} = -\frac{g_{t\phi}}{g_{\phi\phi}}$$ When we take the limit for $r \rightarrow r_{+}$ we have $\Omega \rightarrow \Omega_{Horizon}$.
What do black holes spin relative to? And what happens if you move around it? >There are lots of questions that ask how black holes spin, or how fast they spin, >but as far as I know, none of them address this question.
So the angular velocity of the horizon is the angular velocity of a local non-rotating observer (at the horizon) measured by an inertial observer at infinity. For a detailed discussion, you can find more material on "General Relativity" by <PERSON>. 334