In an answer to this question, the brilliant diagram below was given:
Each fuel has a similarly shaped curve on the chart. What does that signify? what varies along the curve?
I believe Christoph is correct that the curves correspond to mixture ratio.
I can't see an explicit explanation of the arcs in either of the threads where these charts appeared, but the mixture ratio explanation is the only one that makes sense.
Each arc represents a range of oxidizer-fuel mixture ratios for a given propellant. As liquid oxygen (at 1.141 kg/L) is denser than most of the short hydrocarbons, increasing the relative amount of oxidizer increases the average density of the combined propellants, but decreasing the amount of oxidizer improves specific impulse (mainly by shifting the exhaust composition toward simpler molecules, e.g. CO instead of CO2).
An earlier version of the chart appears in a different thread, in which the user Proponent is quoted (from yet another thread?):
Very generally on the top of specific impulse and impulse density, I was thinking about optimal mixture ratios. If oxidizer and fuel have different densities, then impulse density will peak at a mixture ratio corresponding to a higher propellant bulk density than where the specific impulse peaks. The larger the difference in the densities of oxidizer and fuel, the larger will tend to be the difference in the mixture ratios of the two peaks.
... you'd never want to go to a bulk density lower than that of maximum specific impulse or higher than that of maximum impulse density.
The upper-left peak of each arc is the point of maximum specific impulse (it's tangent to the horizontal); going further left would yield diminishing performance. The bottom-right of each arc is the point of maximum impulse density (that is, impulse provided per unit volume, which could also be called "volume-specific impulse").
The individual arcs are not representative of changing fuel temperature; each fuel has a pair of separate arcs, one for basic liquification temperature and one for fuel chilled to the higher of (melting-point-plus-10º) or (viscosity = 3.3cP) -- the chilled fuel arcs generally parallel the warm fuel arcs about a third of the chart width to their right.