What is negative Resistance
Negative Resistances is a behavior in which the current and voltage are inversely proportional to each other.  A normal circuit with a resistor following ohm's law has a current drop, when the voltage decreases. 
In case of a negative resistance, the current increases with a voltage drop.

Practically, there is nothing as a negative resistor. Its just behavior on the V-I graph, where there is a negative slope, and operating in that region would give you a behavior of negative resistance.

In this graph below, you can see the region where the element shows a negative resistance behavior.



I think tunnel diodes and some other kinds of diodes exhibit this behavior.