You should know the sine and cosine for, say, 30 degrees. Say you’re rotating about the y-axis then you’ll rotate the xz-plane. Take the point (1,0,0). This is in the xz-plane (when y=0). Rotate it by 30 degrees about the y-axis. Where should it go? Draw the picture! Do the calculation with the matrix formula you are given, do they agree? Do this for different axes, different angle values, and different points. Eventually you will understand.

Hint: the standard way of drawing a normal graph has the x-axis positive to the right and the y-axis positive up. The right-handed coordinate system has the z-axis pointing out of the paper. This is where your fingers curl from x to y. In this coordinate system, looking down from the positive y-axis into the xz-plane, which direction does going from x to z curl around the y-axis? Is it right-handed or is it left-handed?

Good luck, keep at it!