What does 'per capita births and deaths' mean?
I will use an ever so slightly more specific scenario than what your book offers.



At the beginning of 2017, there were twenty lotus plants in a pond. By the first day of 2018, eight of those twenty lotus plants reproduced. Using this information, we now want to describe the birth rate of lotus plant population. 

To do this, we need the number of plants that produced offspring, and, the population size at the beginning of 2017.

$$\frac{no. \ of \ parent \ lotus \ plants}{initial \ population \ size} = \frac{8}{20} = .4$$

This means that, when considering the twenty lotus plants that first existed at the beginning of 2017, each of those twenty plants contributed an average of 4/10s of a lotus plant offspring for that year. 

To generalize this, we say, "a birth rate of .4 offspring per lotus plant per year." 

The same method and persective can also be applied to the fruitflies, however, they're considering death rate.