Zygarde Cells and Cores are items used to construct Zygarde at a Reassembly Unit.
In order to obtain them, the player first must have a Zygarde Cube in their inventory. Both the cells and cores will spawn over time in any biome and can be found on top or on the sides of logs, leaves and grass blocks. They behave like blocks and don't move around. If not collected by using the Zygarde Cube on them, they will despawn after 10 minutes.
While they share the same shape and base color, Cells and Cores can be distinguished at a glance by the coloration of their eye and core element. On Cells both are green, while Cores have a black spot in their eye and the core element is red.
Trivia
Before 9.1.13 chunks could stop generating cells over time. This happened once the respective chunk had had one or more players spend time inside of it for more than 30 minutes in total. This only applied to the immediate 16x16 area of that chunk though - any active chunks around it were unaffected and would still spawn cells even if the player stayed inside the "dead" one.