To better understand X, Y and Z rotation I'll explain using examples...
X Axis - You're working on a table saw. The bar going through the center of the blade runs left to right (just like the x axis in OpenGL). The sharp teeth spin around the x axis (bar running through the center of the blade), and appear to be cutting towards or away from you depending on which way the blade is being spun. When we spin something on the x axis in OpenGL it will spin the same way.
Y Axis - Imagine that you are standing in the middle of a field. There is a huge tornado coming straight at you. The center of a tornado runs from the sky to the ground (up and down, just like the y axis in OpenGL). The dirt and debris in the tornado spins around the y axis (center of the tornado) from left to right or right to left. When you spin something on the y axis in OpenGL it will spin the same way.
Z Axis - You are looking at the front of a fan. The center of the fan points towards you and away from you (just like the z axis in OpenGL). The blades of the fan spin around the z axis (center of the fan) in a clockwise or counterclockwise direction. When You spin something on the z axis in OpenGL it will spin the same way.