Cells are the beginning of everything. Every living thing is composed and made from cells. Cells are the smallest unit of organization, we know this because many years of cytology has proved this once hypothesis is really a fact. There are two major categories of cellular organization in eucaryotic cells. Those parts which are "membrane bound", called organelles and those which are not "membrane bound". Every aspect of the cell is important because each part or organelle's structure is unique to it's function.
Non membrane bound organelles, are those which provide the membrane itself. They include; the cell (plasma) membrane, the cytoplasm, and the cytoskeleton. The cell (plasma) membrane is made up a phospholipid bi-layer, protein, cholesterol and carbohydrates. It serves many purposes, it is the edge of the cell, it is also the site for chemical activity, and last it separates the living environment. The cytoplasm is the whole cells contents, not including the nucleus, and held in by the plasma membrane. The cytoplasm provides the site for metabolic activity (metabolism) and helps transport molecules and organelles. The cytoskeleton is a supportive and metabolic structure composed of microfilaments, microtubules and intermediate filaments, which are all protein. The microtubules aid in the shape of the cell. Microfilaments are responsible for movement of cells and organelles, an example of this is flagella, a few long projections of microfilaments from the cell surface, this helps in movement (i.e. sperm). The intermediate filaments are strands of globular proteins like the others.
Membrane bound organelles are the "guts" of an eucaryotic cell. Membrane bound meaning that they are enclosed in the cell membrane. The nucleus is enclosed by the nuclear envelope which has two membrane layers. The nucleus is made of DNA and chromosomes and it controls cellular activities via the genes.