What are rates and unit rates?
A rate is simply the measure of the change of some quantity as a function of time. The rate of speed is measured in miles per hour. We might measure the rate of evaporation of water from a hot mug in grams per minute (In reality, it might be a small fraction of a gram per minute). We might also measure a rate of cooling by noting how quickly temperature changes as a function of time.
A unit rate would simply be a change if one unit of the quantity every time unit. For example: one mile per hour, one gram per minute, or one degree per second.
If you are looking at some reference which talks about unit rates, it is probably doing so to make the math simple for estimation purposes. For example, if we know that a glacier creeps along at a rate of about 1 meter per year, how many years will it take for the ice at the middle of the valley to reach the sea 1.2 km away?