I noticed that the values are different if I choose a different base case system. Do the values represent some relative terms?

Yes, HOMER calculates payback by comparing one system with another.  In calculating payback, you are determining how many years it will take to recoup an investment.  You invest a certain amount of money up front, then earn income from that investment, and the payback is the number of years it takes for the cumulative income to equal the value of the initial investment.

But you can only rarely define the "income" of a power system without comparing to some alternative.  If, for example, the system does not need to serve any load, but simply sells power to the grid, then you can define the income of the system simply as the money it makes by selling power to the grid, minus the expense of operating the system.  You could therefore compare the initial cost of the system with its income to calculate the payback.

But in general it's not that simple.  Say you are designing a system to provide electricity to an off-grid house.  A pure diesel system might have low capital cost and high operating cost, whereas a PV-diesel-battery system might have high capital cost and low operating cost.  Neither system produces any income.  In both cases you spend money up front to build the system, then you keep spending money each year to operate the system.  The concept of payback has meaning only if you compare one system to the other.

The PV-diesel-battery system has higher capital cost and lower operating cost than the pure diesel system.  You can define the payback of the additional investment required for the PV-diesel-battery system by comparing the difference in capital cost with the difference in operating cost.  HOMER does exactly that in the Compare Economics window.

So in general, to calculate payback of one alternative we must compare to another alternative.  Even to calculate the payback of the simple grid-sales system that I mentioned above involves an implicit comparison with the base case, which is to do nothing.  The do-nothing alternative is easy to compare to, since all its costs are zero, but if we have an electric load to serve, the do-nothing alternative is not an acceptable one.

A renewable power system designer will often use a non-renewable power system as the base case, but HOMER lets you choose any base case you want.

You could compare a system with two wind turbines to a system that has one wind turbine to calculate the payback of the second wind turbine.  Or you could compare a PV-diesel-battery system with a PV-diesel system to calculate the payback of the battery.