Entropy (I quote from Brian Greene's book "The Fabric of the Cosmos") is a measure of disorder in a physical system.   High entropy means that many rearrangements of the ingredients making up a system would go unnoticed, and this in turn means the system is highly disordered.
Low entropy means that very few rearrangements would go unnoticed, and this in turn means the system is highly ordered."

On this photograph for example, the mango trees are neatly aligned in a straight line and spaced at equal intervals. It represents a system of low entropy, because if one tree was removed and placed say halfway between this row and the next, it would immediately catch our attention.

The geese underneath the trees, on the other hand, represent a system of high entropy. Taking one of them away and placing it somewhere else, would largely go unnoticed.
If there were only two or three geese present underneath the trees, taking one away or shifting it to another spot would of course draw immediate attention. So the more ingredients (geese) a system has, the greater potential it has for high entropy.

In physical systems with many constituents (I quote Greene again), there is a natural evolution towards greater disorder, since disorder can be achieved in so many more ways that order. In other words, physical systems tend to evolve toward states of higher entropy.

Here I leave Greene and follow my own (non physical, layman's) thoughts on this interesting topic, making no apologies if I apply it perhaps somewhat broader than science would have intended.
Curiously, where nature tends to evolve towards greater entropy, we humans try to do the opposite, creating low entropy order whenever we can, because order, "straight thinking", logic, is very much our thing.

Scientists look at a high entropy situation and trace it back to its initial low entropy state and to the rules by which it is governed. And we have done a marvelous job. Look at the abundance of life forms all around us today, and we can trace it now back to its very beginning : the simple joining of two primitive cells.

We walk through a natural forest and there is high entropy all around us. Trees grow where seeds have fallen, blown at random by the wind, or carried within birds until discarded in their droppings. Enter a pine forest plantation or fruit farm and there is nothing but straight lined trees, low entropy, because it makes sense for maintenance and harvesting.
The legendary Jazz singer Tony Bennett once said in a TV interview : "There are no straight lines in nature."

And I believe he is right. Think of a line as being a series of perfectly aligned interconnected dots, a system of very low entropy. Would not last very long in nature!
Wherever man goes he leaves a low entropy foot print, the Dutch hunnebedden in the Northern province of Drenthe are a perfect example. A bunch of large granite boulders strewn around naturally at random would draw no attention whatever, but used to construct a grave and bingo a human low entropy foot print is left behind for thousands of years.

When walking through the bush in outback Western Australia as a geologist during the Nickel boom (1968) I would marvel at the untouched wildness of the place. Then suddenly amongst the rubble strewn around everywhere around me I notice a few flat stones, three perhaps, not larger than a sheet of paper, placed on top of one another. A marker for a mineral claim boundary, a survey point ? A low entropy human foot print, in the middle of a millions of years old high entropy expanse.

From childhood onwards we are taught : order, by our parents, at school, at work, in the army. When finished eating (as a child) and leaving the table you place your chair back properly where it belongs, to restore low entropy. It is still with me, strongly, I judge people by it !

In the Mooloolaba Surf Club the staff do a great job, neatly arranging tables and the chairs around them. Empty plates and glasses are removed immediately. A very aggreeable low entropy environment. Some people enter the Club, sit down have their meal, carelessly shove their chairs back and walk out. Low entropy destroyed. I am annoyed and judge : no education, blunt, careless, oblivious to the comfort of others, little awareness.

I believe that composition (the pleasing arrangements of objects) too is an expression of human's intuitive sense for low entropy. Some of course possess this sense more than others.
My father would marvel at my mother. Every time she entered the lounge room, she would, intuitively, almost unconsciously, move an ornament on a table here, rotate a vase with flowers slightly there, as she walked past it. "It is all perfect again", my father would sigh.

My sister Wivica was in her earlier years an specialist interior decorator consultant for fashionable jewelry shops throughout Europe.
When she applied for the job she was given by her interviewer an object which she was asked to place on a large rectangular table. After Wivica had done that, the interviewer took out a tape measure, and measured the exact position of the object with respect to the sides of the table. "Perfect" he said, "the Golden Cut, spot on!

What does this mean? For human perception even a single object seen within a spacial context (a table, a landscape, etc.) there are only a few low entropy ("just right") positions. In contrast there are lots of "wrong" positions, high entropy, because it does not matter where the object is placed then.

Entropy and Evolution
It is important to recognise that although entropy guides the overall general trend of the development of the universe, it is however subjected to other forces and conditions.
For example Gravity (which pervades the entire universe) tends to cluster particles together into stars and planets. So there can be order even in a high entropy environment.
Brian Greene writes :

This means that just taking entropy as the sole driving force in various philosophical postulations is (at least in my view) over simplistic and not valid.

Disorder and complexity are not synonymous, they are two entirely different things.

Life on earth is very varied and complex, but its evolution has followed a clear directional path constrained by the environment and prevailing conditions. Only those species that adapt and take most advantage of the environment survive. There is complexity but no disorder. The disordering entropy trend is constrained by the prevailing conditions.

Also, for example, the human skeleton is a very complex thing but it follows the exact same design as all other mammals on earth. This points to a clear preferred layout (evolved over time through hit and miss attempts) for a useful and successful skeleton arrangement (See Richard Dawkins : The Greatest show on Earth). Once again complexity, but no disorder.

I never think in terms of entropy when considering the evolution of the universe.
I rather see it as the evolution of the crudest form of blunt energy (the Big Bang) towards ever more sophisticated, eventually living, and through the human species, aware and comprehending energy. There is complexity in this process, but no disorder.
This process (if you like) is driven by a general trend towards higher entropy, but channeled through other forces and local environments towards ever more complex (but in a sense logical and "ordered"), sustainable outcomes.