The simplest answer is to follow the manufacturer’s recommendation. However, as a practical matter, for a thin memory foam topper, it does not matter. For thicker foam pads, it depends on the formula and manufacturing process.
Especially in the case of the older memory foam formulations, the liquid memory foam is poured into a mold and then allowed to solidify. However, during the solidification process, some settling occurs, such that the bottom is a little denser than the top. With thin memory foam toppers, this settling is minimal, and hence difference in density, is also minimal. With a thick memory foam pad, the difference is greater. That is why the manufacturer will recommend that you put one particular side facing up.
With newer manufacturing processes, more advanced techniques are used to create the memory foam mattress pads. There is no settling, and hence no difference in density in the two faces of the foam pad. In this case, it does not matter which side you put facing up. Nevertheless, some of the thicker memory foam toppers or mattresses may use a less stable or less robust formula for the foam. In this case, the manufacturer will recommend that you turn (or flip over) your memory foam topper pad occasionally. It’s sort of like rotating the tires on your car to even out the wear and tear.
Of course, these are issues which affect single-layer memory foam mattress toppers. There are some thicker mattress pads which use two layers – one layer of memory foam; and one layer of firm, high density foam. For toppers or mattresses like this, you have to make sure to put the layer that is made from memory foam on top.