A higher entropy state has a longer description length.
For example, let's say I have a magic electron microscope that can scan and record the exact position and velocity of each particle in some 1-cubic-micron volume, to within Heisenberg uncertainty limits and some finite digitization precision.
If my sample is a 1-cubic-micron volume of flawless monocrystalline silicon at 0 Kelvin, I can 'zip' my recording and transmit that description in a much shorter sentence (in fact, I just sent it to you!) than if my sample is a cubic micron of room-temperature saltwater (whose macrostate I just described, but whose microstate I did not).
If you care about describing the details, you can compress your description better if it's a low-entropy state.
But of course, cosmology is full of more mundane explanations about how the limit of the possible entropy of the universe can grow with time, so a high-entropy state suddenly has a lot of room to increase even further.
