What does increase or decrease in marginal utility mean in terms of quantity demanded?
Typically, we have concave, increasing utility functions. So that means, the more you consume of a good x the more utility you have. However, the marginal utility (the first derivative of the utility function) is decreasing in consumption. So each additional unit of consumption has less additional value than the one before.
A simple example would be food. If you're starving, that first bite of food has the highest utility. But one you get full, additional bites will only have a little additional utility. So the more you consume, the less satisfaction from each additional bite.
In this sense, a higher marginal utility, means a lower level of consumption. That could mean a higher demand.