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Negative resistance devices are typically used as detectors, amplifiers or sources at microwave frequencies. Specifically, IMPATT diodes, Gunn diodes, ISIS diodes and tunnel (Esaki) diodes have regions of negative resistance that are exploited. On a Smith chart, the negative resistance region for reflection coefficients is outside the unity circle. One thing to note about negative resistance: it is usually unstable. That is why it makes a good source for RF signals. There is no simpler way to see instability than on a curve tracer.
The first person that researched negative resistance to be used as an amplifier was Russian Oleg Vladimirovich Losev. A self-taught scientist, he died of starvation during the siege of Leningrad. He also was the first to report LED phenomenon and explain it with quantum theory.
Leo Esaki won Nobel Prize for Physics, for his work in tunnel diodes. He's in our Microwave Hall of Fame.
By definition, a negative resistance device produces power. How does that happen with passive devices like a diode? You have to bias them to a non-zero DC point. On a curve tracer, you are powering the device with test equipment (the curve tracer).
Here's a video of Connie showing off how to make a curve tracer with an O-scope and a few resistors, which took second place in the 2013 MITx 6.002x student contest. First, she shows what a real resistor, and open and a short circuit look like. Then she shows what happens when you connect a capacitor or inductor to the instrument (it forms a distinctive loop). Towards the end, she tests an op-amp circuit that is configured for negative resistance. It is perfectly stable and well behaved, nothing like a microwave diode. At the end you will see the trace of a tunnel diode. In a specific region you can see negative resistance; you can also tell that the device is unstable here (it is oscillating). Along the way, you will observe the effects of power supply noise! We love this video, it speaks to first principles in engineering, and laboratory verification, and is well explained by an enthusiastic presenter.
Connie shows how to make a breadboard curve tracer, then shows negative resistance examples
Go here to learn more about curve tracer measurements. Unless you have decided you want a career in antennas, which are boring compared to negative resistance... perhaps you will enjoy this video.