How does Reynolds Number affect skin friction drag?
First of all, friction is bad for efficiency. It slows moving things down and needs a constant energy supply to be overcome. The more friction, the more energy has to be supplied, and this energy is lost as heat.

Aerodynamic friction is caused by viscosity. The Reynolds number tells you how big viscosity is in relation to inertial forces. A bigger Reynolds number signifies lower viscosity. This means a higher Reynolds number almost always results in lower friction. If you look at the plot below, the downward trend can be easily spotted.


Friction drag coefficient of a flat plate over Reynolds number (picture source). Note the double logarithmic axes.


  Is there something like " higher Reynolds number, higher drag force " stuff ?


Yes, sometimes. Please look at the transition curve: Here a flow which is initially fully laminar slowly changes with increasing Reynolds number into one with a laminar start and a transition to turbulent flow somewhere downstream. This adds a section of turbulent boundary layer where at a lower Reynolds number the flow would had been laminar. You will notice that for the same Reynolds number, a fully laminar flow (lower line) is much less draggy than a fully turbulent one (upper line). Therefore, replacing some of the laminar flow with a turbulent one will result in more drag.

Now I need to explain why increasing the Reynolds number leads to more turbulent flow. For this, I turn to this answer:

Inside the laminar boundary layer, small disturbances become less and less damped the higher the local Reynolds number becomes, and at a Reynolds number of around 400,000 in unaccelerated flow some frequencies become unstable (see Tollmien-Schlichting waves) and will eventually create so much cross movement that the boundary layer becomes turbulent. Now parcels of air which flow at high speed in the outer part of the boundary layer will move close to the wall and kick the slow parcels there ahead, greatly reducing the deceleration of the flow close to the wall, at the price of slowing down and expanding the whole boundary layer.

Simply put: A laminar boundary layer cannot be sustained indefinitely but will change to a turbulent one if the Reynolds number is high enough. This will swap some of the previously laminar portion of the boundary layer to a turbulent one, increasing drag.

While all of the above is only strictly true for flow over a flat plate without a pressure gradient, real flow will complicate things again: Now turbulent flow is not all bad; the example of the dimpled golf ball shows that a turbulent boundary layer in flow with a pressure gradient can also lead to lower drag, given the right circumstances.