What causes contact resistance? When two components are combined in an electric circuit, there is apart from their own resistances a contact resistance at their junction. This causes a sudden voltage drop of  $V_{drop}=R_{contact}I$.
Another (and unrelated) property is thermal resistance, which is simply a measure of a materials resistance against heat flow. Contact resistance in this field is also present, as the temperature drops a bit extra at the interfaces.
Total resistance in both electric and thermal series combination is:
$$R=R_1+R_{contact}+R_2$$
Let us in both the electric and the thermal case assume direct contact of the two conductors (clamped together, not soldered or alike). Resistance within a material is for an ideal, simple model intuitively clear - electrons, particles etc. bumb into lattice ions and exchange energy.
My question: What is an intuitive explanation of the sudden loss because of contact resistance? How is contact resistance explained?
 A: This is a very interesting question, especially considering the very recent history of scholarship on electrical contact resistance (a term first coined in 1964 by William Shockley, one of the inventors of the transistor), as well as thermal contact resistance. For the following explanation, I will use this research paper on electrical contact resistance published in 1993. In this paper mathematical models of contact resistance for electrical and thermal contact resistance are provided, but here some intuitive explanations are provided.
Now, when electrical current traverses from one medium to another, surface contaminants interfere with the flow of electrical currents. The electrical current must give up some energy to traverse from one medium to another. This can be seen from the model of contact resistance used within the paper.
$$
R_\text{contact} = \left\{ (\rho_1 + \rho_2)(1/[4na]+\alpha^{-1}) \right\} + \rho_f s / A_c
$$
Here, the $\rho _f$ is the resistance of the film between the surfaces; $\alpha$ the thickness of the contaminant. The first part of the equation is due to constriction effects, the second due to surface contaminants. Hence, there are two physical effects at play,


*

*Constriction effects enforced when going from one medium to another, which inevitably leads to loss of energy

*Surface contaminants which interfere with the flow of electrical current
A: 
Another term is thermal resistance,

This is incorrect. Thermal resistance is something that prevents heat flow. It is an entirely separate concept from electrical resistance.

How is contact resistance explained?



*

*To obtain very low resistance in a material like most metals, the electrons must be delocalized from the individual atoms, and free flow around in material. When two pieces of metal are apparently touching, they might not be in such intimate contact that electrons can flow freely between them. In fact, if they were we would likely consider them as welded together.

*Two touching surfaces might not be ideal. There might be oxides on the surfaces, or dirt. 

*The two surfaces are not perfectly smooth, so the area of intimate contact is much smaller than the macroscopic area of the two surfaces. Even a a few microns of axial length can introduce measurable resistance if the cross-sectional area is small enough.

What is an intuitive explanation of the sudden loss because of contact resistance?

It doesn't really matter that the interface area is very thin (in the direction the current is flowing) Any situation where electrons must give up energy to pass from one location to another, no matter how thin a region its localized to, will look like a resistor when analyzed as a circuit element. 
A: Although there are several sources of contact resistance, the main source of  contact resistance is the oxidation of the contact surfaces.
For the electrical case, the oxides of the materials have a much lower electrical conduction (higher resistance) than the materials, therefore the contact area (that is not cleaned and protected) will have a higher electrical resistance that the given materials.
For the thermal case, the response is the same as above, except  "thermal" is substituted for "electrical."
The best "intuitive" example I can think of, is two "hard surface" roadways with a section of sand between them.  It will be easier to run on either of the hard surfaces, than on the sand. You end up using more energy on a given distance of sandy roadway than on an equal distance  of hard roadway.
A: Indeed the contact resistance can be, as discussed in previous answers, attributed to surface features in terms of asperities and passivating layers. The behaviour of these barriers to conduction depends on contact pressure. Passivating layers are oxides and hydroxides that ubiquitously form on conductor surfaces, and pose a barrier to electron transport. While the presence of roughness features restrict conductance to a limited region of true contact area, the extent of which is substantially smaller than the nominal contact area. Conduction mechanisms through passivated layers (tunneling) nanocontacts at fine asperity to asperity contact (ballistic transport) and the conventional ohmic contacts of larger patches of true contact combine to give rise to the observed electrical contact resistance ECR.
source
more details here
A: An intuitive answer could run along the following lines.
When any two dissimilar electrical conductors (say, A and B) are brought into contact, the distribution of the charge carriers in A and B at the junction gets altered so as to assume a new equilibrium distribution. This new distribution of charge carriers changes the potential drops from A to air (delta V1) and B to air (delta V2), that existed before the junction was formed, to a new potential drop delta V. This potential drop delta V causes an additional resistance to the flow of electricity across the junction.
Since electric current flow and heat flow are governed by similar laws, we find an addition resistance to flow of heat, at junction of dissimilar thermal conductors.
Neither impurities nor oxides etc need to be invoked to explain the additional resistance at the junction of two dissimilar materials.
A: There is not a truly simple answer that can be posted on a web site in a few minutes to the last question that was asked by the OP: "How is contact resistance explained?"  This is easily shown by reading, for example:
Heinz K. Henisch.  Semiconductor Contacts: An Approach to Ideas and Models.  Oxford Science Publications, 1984.
