What each major organelle does
Eukaryotic cells divide labor among membrane-bound compartments. The nucleus stores DNA and directs gene expression. Mitochondria generate most of the cell's usable energy (ATP) through aerobic respiration. The endoplasmic reticulum (ER) comes in rough form, studded with ribosomes for protein synthesis, and smooth form, involved in lipid synthesis and detoxification.
The Golgi apparatus modifies, sorts, and packages proteins and lipids for delivery. Lysosomes act as the cell's recycling and digestion centers using acidic enzymes, while peroxisomes handle specific reactions including breakdown of certain fatty acids and neutralization of reactive byproducts.
How the organelles work as a system
These compartments are interconnected rather than isolated. Proteins made on the rough ER travel to the Golgi for finishing and then to their destinations, and vesicles shuttle material between compartments and the cell surface. Mitochondria and the ER also form close contact sites that coordinate calcium signaling and lipid exchange.
Thinking of organelles as a coordinated supply chain captures cell function better than viewing them as separate parts. This is general educational information about cell biology.