This is what happens when some kind of new compound is formed between these two, here it'll be series of sulfuric acid-water complexes. Same thing happens with metals when intermetallic compounds form, see titanium-nickel phase diagram. Normal case would be eutectic, see aluminum-silicon phase diagram
My uneducated understanding is that the chart shows at which temperatures sulfuric acid freezes depending on the concentration. Also in my very basic understanding of physics and chemistry I would have thought that it's linear or exponential or something predictable and not that jumpy.
In normal cases you'd see two curves going away from pure compounds downwards to a common minimum, which is eutectic point. It's generally only vaguely predictable, but always monotonic
Sulfuric acid and water has various H2SO4 and H2O ratios. So like 1 H2SO4 and 6, 3, 2, or 1 H2O it also has just the H2SO4 and H2S2O7. These are present as local points within solutions and with different prominence depending on the amount of water added. These 8 different ratios each have different freezing points.
If I had to guess, I would assume that there are different molecular lattices that sulfuric acid and water can form at different concentrations and that these different lattices have different freezing points. I will now go look it up.
What you're describing are different crystalline phases of pure compounds, but this does not give you new minima, you need some new compound to form for that