Half sets are a tricky but important concept! There is a nice summary in cryoEM 101 and I wrote a short summary in another post, but to answer your direct question: they are a little bit like a train/test split, but instead of creating a single model and testing it against data it didn’t see, we create two models and compare them to each other. This gives us a good estimate of the resolution we can trust.
So yes, since we don’t know what resolution we can trust in heterogeneous refinement, it is good practice to keep the particles downsampled so that only lower resolution information is available to the alignments. It also helps with memory and speed 
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Notably, RELION solves the problem of overfitting in 3D classification/heterogeneous refinement in another way by giving the user a tunable parameter (“T”, the regularization parameter), but we’re all trying to solve the same problem.