This is a basic fact of science that I remember always getting reminded of again and again when in school. In terms of levels of organization, it goes from biology to chemistry to physics to math the deeper you go into each respective science.
In the same way, the levels of organization from the organism to the atom go from biology to chemistry to physics (we don't go deep enough to hit pure math yet! :-) ).
Let's start at the organism level. I'm assuming that we're going to be talking about a multicellular organism like, say, a human. Let's start at the biological level.
At the top level, we have the full organism, itself. This organism will be composed of organ systems, much like how humans have the cardiovascular system, the respiratory system, etc. These organ systems will generally be separated most easily by physiology (function), but often by anatomy (structure), too.
Each organ system is composed of separate organs, the entities that carry out distinct functions in the organ system. Again, these are often separated physiologically (what they do), and sometimes by anatomy (where it's at). Sometimes the distinctions are obvious: You can tell easily where the heart ends and the blood vessels begin, the valves. Sometimes they're not, like looking at the macroscopic intestine and determining where the jejunum ends and the ileum begins.
Each organ is then going to be made of separate tissues. These tissues take the organ's discrete set of functions and perform a certain subset of them or perform support functions for other tissues in the organ. For example, in the heart, you have endocardium (internal lining), myocardium (muscle), epicardium (external lining), blood vessels, electrical conduction pathways, etc. Each of those tissues contributes something to the heart's overall function of pumping blood to the body.
Each tissue is made up, then, of cells, the most basic unit of life. Each cell performs a certain function in the tissue, and the sum of the cells' actions create the overall action of the tissue. For example, in the myocardium of the heart, cardiac muscle cells individually contract. When each all cells contract as a unit, the heart is able to pump. The way each cell contracts at the same time is through each cell "talking" with its neighboring cell. In that way, the cells of the myocardium individually contribute to the overall action of the heart's muscle tissue.
Now, we delve deeper and look at the organelles of each cell. The organelles each perform different cellular functions. Most of the time, though, they either build molecules, transport things, or break molecules down. By doing this, the organelles produce energy for the cell, or they act as the cell's manufacturing centers for things.
At this point, we've reached the limit of biology, and we're going into chemistry. The next level down is that of the macromolecules, long sugars, proteins, fats, or nucleic acids. Something cool? That's all there is, nothing more, nothing less. Moving on:
Each macromolecule is composed of individual molecules. For example, in a protein, there are multiple amino acids, which are its basic building blocks.
Finally, we're right at where chemistry and physics intersect. Each molecule is composed of individual atoms. Generally, in biological systems, the vast majority of atoms will be carbon, oxygen, hydrogen, nitrogen, and phosphorus.
It's all pretty simple in the end, isn't it? I hope that helps!