Are you familiar with the Boltzmann distribution (the title of your post suggests you are)? This tells us how different energy levels are populated at a given temperature. If there are N_{0} molecules in the ground state, then the number N_{E} in a state of energy E is given by

N_{E} = N_{0}e^{-E/kT}

Thus the higher the energy E, the less populated the state is.

Consider the system with energy levels 100k apart (write small k for Boltzmann's constant, so it doesn't look like a temperature of 100 K). At a low temperature, say 10 or 20 K, where E>>kT, there are very few molecules in the excited states. If you increase the temperature by 1 K, "very few" becomes "very few plus a tiny bit more". The increase of energy due to this "tiny bit more" going to a higher level is very small, so the heat capacity (energy input to raise the temperature by 1 K) is also small. As the temperature rises, and the population of the higher levels increases, the heat capacity also increases.

Now consider the system with levels 20k apart. The higher levels are easier to reach, and at 10 or 20 K, they are already significantly populated, and more molecules are promoted for a given increase in temperature, so the heat capacity is higher than for system A at the same temperature.

System C is different, in that you have a few closely-spaced levels, then a big gap, then a few more closely-spaced levels, and so on. At low temperatures we can assume that the 200k level and above are essentially unpopulated, and what we have is a system of 5 levels 20k apart. To begin with, it behaves like system B, but there comes a point when, in system B, levels 100, 120, 140 etc. would start to be populated, but in system C these don't exist. For a finite system, at high temperature the levels would tend to become equally populated, with little change with increasing temperature, so the heat capacity would tend towards zero. That's why you see the peak in Cv and the decrease at intermediate temperatures (note, Cv is not negative, the slope of the curve is negative). Of course, the system is not really finite, and as T increases further, the higher levels (>200k) start to be populated and contribute to the heat capacity, so it rises again.