The Second Law of Thermodynamics can be stated in any of three synonymous ways:
For a spontaneous process, the entropy of the universe increases.
For a spontaneous process, ΔSuniverse > 0.
For a spontaneous process, ΔSsystem + ΔSsurroundings> 0
Ultimately, for any spontaneous process the entropy, which is related to randomness or disorder, of the universe increases. Entropy is covered in much greater detail in the next lesson (18.2 Entropy) but that it correlates with disorder will suffice for now.
The last statement of the Second Law of Thermodynamics divides the universe into two parts: the system (what you're investigating) and the surroundings (everything in the universe besides the system). In chemistry the system is often a chemical reaction under investigation. To be clear the Second Law does NOT mean that ΔSreaction must be positive as ΔSreaction is just the ΔSsystem which can be either positive or negative. But if ΔSreaction for a spontaneous reaction is negative, then the Second Law does mean that ΔSsurroundings must be positive and of greater magnitude in this example so that ΔSsystem + ΔSsurroundings > 0.
In one sense you can view the Second Law of Thermodynamics as being the most important of the three; in the sense that it is the one most commonly tested upon in this chapter and students should recognize it in any of the three forms presented above.