Why did eukaryotic cells evolve? (Not asking how)?

The defining feature of eukaryotes is the membrane bound nucleus, but there are other important aspects. Membrane bounded organelles enable a higher precision of functions at the price of slower reproduction. The eukaryotic chromosome has multiple origins of replication allowing vastly increased genome size, and sexual reproduction allows rapid recombination.

The evidence indicates that eukaryotic cells appeared more than a billion and a half years ago. The protists (not archaea) are a diverse group of organisms generally defined as eukaryotes that do not form multiple specialized cell types. They can be grouped into six major groups based on molecular features, and their patter of diversification from the ancestral group can be determined much in the same way that the prokaryotes can be divided into eubacteria and archaea. The plant-like protists (algae) divided from a group that would become both animal-like protists (protozoa) and fungi. Those three groups went on to develop multicellularity.

You can look at the development of multicellularity through colonial organisms. Some complex colonial organisms have specialized cells (e.g. Volvox). Then there are sponges which have multiple specialized cells, but not tissues; if you pass a sponge through a sieve that breaks it into individual cells, the cells will reorganize into a sponge.

In each of these steps, the feature is that the organisms become bigger. Bigger organisms are resistant to being eaten by smaller organisms. When a small single-celled alga was placed in culture with a larger single-celled predator, the algae that formed clusters survived and hit an optimum at eight cell clusters. The trait was conserved in the absence of a predator. In yeast (fungi), multicellular clusters developed from single-celled organisms develop specialized cellular functions rapidly.

While becoming bigger is important, the geologic history of Earth points out some of the reasons that it was a billion years from early eukaryotes to complex life (not exactly the timeframe described as "poof"). The Earth was mostly frozen for some of the time (Cryogenian period), and until there was abundant free oxygen, animals and animal-like protists could not thrive. A second consequence of an oxygen rich atmosphere is an ozone layer, which makes land the most sunlight-rich water, the surface, habitable.

If you aren't interested in how, but only want an alleged why, they you need to ask in the religion or philosophy sections.