So firstly, I would define relative prices as 'the price of a good or service compared to another good or service.'
In a competitive market economy, explain one factor that might cause a change in relative prices.
Here I would then discuss microeconomic demand factors, as you need a factor that increases demand in a single market (rather than on a macro level) for relative prices to increase. Say for example, a particular g+s comes into style, then more people will demand it. Given that the demand for other g+s in other markets stay relatively stable, the price of the 'cool' g/s will rise relative to other g+s.
Explain how a change in relative prices would result in a reallocation of resources.
I would start here by defining the price mechanism as 'the system whereby the free forces of demand and supply interact to set relative prices at the point of market equilibrium.'
Then talk about how a rise in the relative price of a g/s creates a price signal for producers, signalling underproduction and hence more profit opportunities. As such, to take advantage of these opportunities, firms will wish to allocate more resources to its production, and they will allocate their resources away from other markets where relative prices have fallen.