How did cyanobacteria contribute to the evolution of multicellular organisms like the plants and animals we see today

Cyanobacteria had a role in the evolution of eukaryotic cell, more precisely their organelles. It has been shown that chloroplast, cell organelles found in some eukaryotic lineages, which are specialized in performing the photosynthesis evolved from cyanobacteria through the process called endosymbiosis. In this process, photosynthesizing cyanobacteria was engulfed in some ancient eukaryotic cell. Eukaryotic cells have evolved from the endosymbiotic events.
By producing and releasing O2 (as a byproduct of photosynthesis), cyanobacteria are thought to have converted the early oxygen-poor, reducing atmosphere into an oxidizing one. This caused the Great Oxygenation Event which dramatically changed the Earth's life forms and led to the formation of multicellular organisms.

Interacting group of various species in a common location. for example, a forest of trees and undergrowth plants, inhabited by animals and rooted in soil containing bacteria and fungi, constitutes a biological community.