The coefficient of friction is defined formally as the ratio of the force required to move two surfaces over each other, and the force pushing them together. The coefficient of static friction, the ratio when objects are at rest, may be different (and significantly higher) than the coefficient of kinetic friction, when they are in motion with respect to each other.
One way we can see this is by having the two surfaces at an angle with respect to gravity. By changing the angle, we change the force acting on the surfaces. We can see that as we increase the angle, and thus the force, the box or block will start to slide down the surface. Once it is in motion it will continue to slide, even if the angle is decreased slightly; the kinetic friction is less! But interestingly, it is unaffected by changing the mass of the box, since while the total mass and force may change, the ratio stays the same.
You can experiment with this at home; find any rigid surface that you can prop up to change the angle, and find flat-bottomed containers that can rest on it or slide down it, then add mass to the containers to see what happens. Compare the effects, if any, of changing the mass, the angle of the slope, and the material of the containers.
Then, compare your results to what you find from a simulation, like this one by Tom Walsh: Static and Kinetic Friction on an Inclined Plane. You can change the mass, the coefficients of friction, the angle, and even the force of gravity (in case you want to see what your experiment would look like on the Moon). Also, try giving your mass an initial velocity up the slope – does friction slow it down? What happens after its velocity reaches zero?