A unit rate simply means how many of one type of units you get per 1 other type of unit. Examples of that: [tex] 300\frac{l}{ s } [/tex]
This is rate of fluid flow of some pump for example. It pumps 300 liters every second.
Other example: [tex]50 \frac{km}{h} [/tex] This is example for speed. Somebody is moving at 50 kilometers per hour (every hour he travels 50 kilometers)