The general theory is that proteins started to replicate, kind of like prion disease now, before developing cell walls. These became Prokaryotes, the simplest cells. Life spent almost two billion years in just this form.
Later, they evolved to eukaryotic cells with a separate nucleus and secondary cell structures like mitrochondria. It is thought that the eukaryotic cells were the result of a division or combining accident, leaving more separate cellular machinery in the cell that then specialized.
Only eukaryotic cells had the energy production and specialization of function that made multi-celled life possible. After eukaryotic cells appeared, soon after, multi-celled organisms and what we'd consider animals beyond bacteria started to evolve.
The rise of eukaryotic cells only happened once in two billion years, and this is so unusual that it is thought to be the Great Filter, the event so unlikely that most life doesn't evolve to that point, which could explain why there are no aliens. Most planets with life in this scenario are thus filled with single celled organisms and nothing more complex.