In physics, we distinguish angular momentum and linear momentum. Both of these are vector quantities - and while that makes sense for linear momentum, it is initially a surprising concept for angular momentum. How do you give a "direction" to something that is rotating?
The answer is - you point along the axis of rotation, because that's the only direction that is constant while all the points in the rotating object are moving in different directions. Once we have the axis defined, we need a convention for the sign: when I look at an old-fashioned vinyl record player, does the angular momentum vector point up, or down? Now the record rotates in a clockwise direction - and if I hold my right hand so my fingers point along the direction of rotation, then my thumb is pointing down.
In the case of the wheels on a car, that means that the wheels on the right hand side, which rotate clockwise as observed from the side, have their angular momentum vector pointing into the car (to the left hand side of the car). On the left of the car, the wheels appear to be rotating counter-clockwise, and the angular momentum vector points out (which still means "to the left of the car").
Now when I have a rotating object that is subject to torque (which can also be described as a vector quantity), then the object will change its angular momentum and this change in angular momentum will follow the normal rules of vector addition: if the torque vector is aligned with the angular momentum vector, the object will accelerate (start to spin faster); if it is pointing 180° the other way, the object will decelerate (slow down); and if the torque is pointing in any other direction, it will result in precession: that is, the direction of the spinning axis will change in a way that is initially not at all intuitive. That's how gyroscopes can be explained...