Is there a sense in which this is something of a riddle? Surely we as humans perhaps lack the capacity to perceive the ultimate in our lives. However, this saying points towards the way in which in our relative lives, there are moments of insight or epiphany when we are able to sense the ultimate reality that governs our existence. The contradiction or paradox in this saying therefore points towards the way in which we can grasp towards understanding and enlightenment.
While the Relative is the Subjective, the Ultimate is not necessarily the Objective. We see things based on our Subjective biases and opinions, and thus they are Relative to those of other people. However, our Ideal or Ultimate will not be a truly Objective "Best," as our Ultimate is also Subjective. It's not an easy thing to define, but I would posit that we can find our Subjective Ultimate in our equally Subjective Relative by applying our experiences and knowledge in a way that we believe to be correct and true. We can, to a certain extent, accept the Objective in that it will be true regardless of opinion, but we will still deny that the Objective has any effect on our personal Ideal Ultimate.
I can imagine several ways of answering this question. In one respect, this phrase might be a good slogan for agnostics. Because agnostics doubt that there is any absolute proof of such metaphysical "ultimates" as God, but because they may accept the value of such ultimate ethical values as "the Golden Rule," they may find good reasons for accepting "the Golden Rule" precisely because there may by no ultimate source of metaphysical truth, such as "God." An agnostic might find the "ultimate" ethical value (the Golden Rule) convincing precisely because metaphysical claims seem merely relative and unconvincing. Here's a specific example: Christians, Jews, and Muslims may disagree about "ultimate" religious claims, and those claims do not seem open to the standard forms of proof. The truth-status of such claims thus seems relative. Precisely for this reason, it makes sense for members of different religions to find some "ultimate" ethical value in something like the Golden Rule so they can at least live on the same planet in peace.
To me, the ultimate means the best, the epitome of whatever you are considering. If it is relative, it cannot be the best as it is always being compared to something else, so it is the best only within that comparison. Therefore, if you find that the ultimate is always relative, there is room for interpretation and movement, not just one simple, ultimate answer. Life takes on a different look when you believe that everything is relative, without the hard and fast rules or lines in the sand that some people draw. More of your own judgment is required.