What is cytoplasmic localization?
"Cytoplasmic localization" is a very general term and it means that something is present in the cytoplasm. For instance (hypothetical but there are known examples), you can say protein-X is localized to cytoplasm or the cytoplasmic localization of protein-Y is reduced upon phosphorylation. Similarly, there are terms like "nuclear localization", "ER localization", "mitochondrial localization" etc.

The usage mentioned in your excerpt is actually unclear and misleading. There is no process called cytoplasmic localization. What it actually means is that there are proteins/RNA inside the cytoplasm of the embryo that are asymmetrically distributed. When the cell divides, these molecules are therefore asymmetrically sorted to the daughter cells. Depending on what (and how much of) molecules the daughter cells receive, different cells adopt different phenotypes. Also note that the axis of division also plays a role; if lets say the distribution of a given molecule is asymmetric only about the anteroposterior axis and the division happens along that axis then both daughter cells receive the same amount of molecule and both the cells would be similar (w.r.t that molecule). This won't be the case if the division is along left-right axis. See the figure below.


  
  From: Berika et al., 2014


I am not sure which book you are following but Developmental Biology by Scott F Gilbert is a good book and explains these processes nicely.