The first law of thermodynamics is the application of the conservation of energy principle to heat and thermodynamic processes:
The change in the internal energy of a system is equal to the heat added to the system minus the work done by the system

The first law makes use of the key concepts of internal energy, heat, and system work. It is used extensively in the discussion of heat engines.

• A heat engine typically uses energy provided in the form of heat to do work and then exhausts the heat which cannot be used to do work.
• Thermodynamics is the study of the relationships between heat and work.

“The entropy of the universe increases during any spontaneous process”
The “universe” just means “the system you’re looking at PLUS its surroundings”, i.e., everything that’s close around it.

What Is Entropy, REALLY?

Entropy measures the spontaneous dispersal of energy:

• how much energy is spread out in a process, or how widely spread out it becomes — at a specific temperature.
• Sometimes, it’s a simple equation,
• Entropy change = “energy dispersed”/T

or

• Entropy change = q_reversible/T
  

as in phase changes like melting or vaporization where DS = DH_f /T or DH_v /T, respectively. The second law is based on human experience.  It doesn’t come from complicated theory and equations. 

Think of these experiences that you may have had: 

You will fall if you climb up a rock and then let go. 

Hot frying pans cool down when taken off the stove. 

Iron rusts (oxidizes) in the air. 

Air in a high-pressure tire shoots out from even a small hole in its side to the lower pressure atmosphere. 

Ice cream melts in a warm room. 

What’s happening in each of those processes?

• Energy of some kind is changing from being localized ("concentrated" in the rock or the pan, etc.) to becoming more spread out.
  
• Look at those examples again to see how that statement fits them all.
  

OK?  That’s it — a simple way of stating fundamental science behind the second law:

Energy spontaneously disperses from being localized to becoming spread out if it is not hindered from doing so.

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Over time the temperature of the ice cream and the temperature of the room become equal.

The entropy of the room has decreased and some of its energy has been dispersed to the ice cream.

However, the entropy of the system of ice cream has increased more than the entropy of the surrounding room has decreased.

In an isolated system such as the room and ice cream taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy.

Thus, when the 'universe' of the room and ice cream system has reached thermal equilibrium, the entropy change from the initial state is at a maximum.

The entropy of the thermodynamic system is a measure of how far the equalization has progressed.