Basically, it states that the total entropy of any system plus that of its environment increases as a result of any natural process.
Since entropy is a measure of disorder, this basically means that for any lawful thermodynamic process, the disorder of the universe as a whole (system + environment) must increase. For those unaccustomed to physics, entropy (disorder) can be a subtle concept. I can offer you examples that come from the source listed below.
A jar containing separate layers of salt and pepper is more orderly than when the salt and pepper are all mixed up. Shaking a jar containing separate layers results in a mixture, and no amount of shaking beings the orderly layers back again. The natural process is from a state of relative order (layers) to one of relative disorder (a mixture), not the reverse. That is, disorder increases. Similarly, a solid coffee cup is a more "orderly" object than the pieces of a broken cup. Cups break when they fall, but they do not spontaneously mend themselves. Again, the normal course of events is an increase of disorder.
So, back to our original problem, let's call an organism the system (which again, is simply the object that we wish to consider). Clearly, a human being is a highly ordered organism. As with the salt and paper, taking all the molecules that make a human and shaking them around for a billion years would simply not create a human. What's more, the process of growth is one of increasing order (decreasing entropy) as we move from a single cell to trillions of specialised cells. Similarly, evolution (in its broadest sense) has analogously moved from simple macromolecules to complex organisms, which is a clear case of increasing complexity. Do these processes violate the second law of thermodynamics?
No, not at all. Remember that the entropy (disorder) of the organism PLUS its environment (i.e. the universe) must increase for the process to obey the law of thermodynamics. When we grow (or evolve), we do so by taking in highly ordered food and breaking it down into simple molecules without much order (metabolism), which we then excrete. These simple molecules that we push into the environment thus represent high disorder or entropy. This increase in entropy of the environment is MORE than the decrease in entropy within us.
Therefore the process is 'lawful': the entropy of the system PLUS the environment does increase. And so as with the first law, we live at the expense of the universe - we are localised examples of an increase in order that are made possible by increasing the DISORDER of the universe.
Reference: "Physics" (5th edn.) - Giancoli