the coefficient of friction
The coefficient of friction is a single number that says how 'grippy' or 'slippery' a pair of surfaces is. Rubber on dry concrete has a high coefficient (grippy); ice on steel has a very low one (slippery). It is the number that turns 'how hard the surfaces are pressed together' into 'how much friction you get'.
The coefficient of friction, written mu (the Greek letter, said 'mu'), is the ratio of the friction force to the normal force between two surfaces. There are two versions: the static coefficient mu_s sets the maximum grip before sliding, f_s(max) = mu_s times N, and the kinetic coefficient mu_k sets the drag while sliding, f_k = mu_k times N. It is a dimensionless number (no units) because it is a force divided by a force, and it depends on both materials in contact, not on either one alone.
Typical values range from about 0.01 (very slippery, like ice) to around 1 or more (very grippy, like rubber on rough asphalt). Usually mu_s is a bit larger than mu_k for the same pair of surfaces. These are experimental, approximate values: real friction depends on cleanliness, roughness, temperature, and moisture, so treat table values as good estimates, not exact constants.
For rubber tires on dry road, mu is roughly 0.7; on wet ice it can fall below 0.1. That is why the same braking that stops a car quickly on dry asphalt sends it sliding on ice.
A larger coefficient means more friction for the same normal force.
The coefficient of friction is dimensionless and depends on the pair of materials together. To good approximation it does not depend on the contact area or, for kinetic friction, on the sliding speed.