What is opportunity cost? A matter of life and death.

Opportunity cost is simply the cost of producing a good with reference to what you could have instead produced in the meantime.

You can understand it in terms of the number of hours you have in a day (time is incidentally usually a factor which has to be taken into consideration, along with resources when considering opportunity cost). If you have 12 hours in a day that you can do something useful in, you can do different things. Work, eat, socialise etc.The value of each activity to you as a person may be different, it may even change depending on the number of hours of each thing you do.
If you work for 2 hours you might get 30% of the work you need to do done. Working for another 2 hours might only get you up to 40%, so perhaps you might have better spent those hours resting, or doing something else, so that you can increase the value of the hours you use to work later in the day.
This is a crude explanation of why people take breaks in revision, from an economics perspective.

Another interesting thing to link opportunity cost to, is the production possibilities frontier. Its called a frontier, because it literally is a graphical frontier - a line which divides the areas of the graph where a production point can exist from those that cannot. You can think of the production point as a person on a battlefield. They will have different advantages and disadvantages at different points, perhaps the terrain gets rougher as they go further away from their base. Perhaps they can even cross over into no man's land while still being able to handle the increased difficulty in moving and hiding. It is probably advantageous for them to go further and further away from the base since they will be closer to the enemy and better able to target them. However, if the man decides to stand directly in front of the enemy trench or front line then he is very likely to either get shot cleanly in the face, or simply be taken hostage. The idea is that as the man gets further away from his own base, he is able to aim more accurately (produce more damage), up until a point where he is at the verge of being shot or captured.
Say that there are two enemy bases which he can shoot at, if the man were able to get into a position where he could shoot at just one base, it might not be as efficient, since he would only be able to shoot based on the probability of enemies being in vulnerable positions in one base. If he were as close to the other base as well, while he wasn't shooting at the first base, he could be shooting at the second base, and maximising his DPS (damage per second) - again, doing the same amount of damage in less time is of more intrinsic value (or detriment if you are the enemy). This is gradually become a discussion which sounds more like it is describing a video game than an actual battlefield, but never mind.
So, the man has a problem now. The closer he gets to the other side's base, the further he has to move away from the base he was originally shooting at, because his distraction level is increased by shooting at two bases at the same time. We could in fact draw the two bases on a map and show the limits of the man's reach:

So where is the man's optimum position? Clearly it is the place where he is closest to both bases in terms of distance and where he is ideally safe. We note that if the man travels upwards, he gets closer to the first base, but if he travels right he gets closer to the second base, without affecting his distance from the first base (assuming they are both very long). The man is safest (expends the least amount of effort and produces the least amount of damage) behind his trench in the friendly base.
We note that the red line is the limit of the man's reach. He could be anywhere behind that line. We note that the line is not straight, because the danger and struggle the man faces is not simply linear (it does not increase proportional to) the distance from either base. In fact, it is much more like the force experienced by a negative charge as it approaches an electron, or the force you experience when you press down on a spring, or folding a piece of paper into halves again and again and again. At first it is easy, but as you make progress you get diminishing returns for the same amount of effort you put in (in the case of the electron you would get less distance gained, in the case of the spring, the spring would not get much smaller and in the case of the paper, you would eventually be unable to fold it in half again even though you were trying much harder than you were before).

We can see that because of the diminishing returns the man gets when he tries to approach either of the enemy front-lines, he could substitute some of his gains in one direction for larger gains in the other direction - meaning that he could sacrifice some distance to the orange base for perhaps double the distance to the yellow base. Where is the optimum position? It is where the sum total of the distance to each base is lowest.

The optimum point (assuming that the value of the distance to the bases is proportional to the distance - unlike the danger) is simply the point where the sum of the distances to each base is lowest, or equivalently, the sum of the distances from the man's base in the upwards and rightwards directions is greatest.
If you like maths, you may be thinking that you know exactly how to solve this problem. A common mistake people make is to say that the problem can be solved by finding the point which maximises the radius (or absolute distance from the friendly base). This is incorrect and can be explained by reference to the Pythagorean Theorem, where:

$$x^2 + y^2 = r^2$$

Note that here, if we maximise r, then we are maximising $x^2 + y^2$ rather than $x+y$ (assuming x represents the distance in the rightwards direction and y in the upwards.
Rather we can write:
$z=x+y$
And then we could do partial differentiation with respect to two variables and find the maximum that way.

Linking this back to the production possibilities frontier, the frontier, as you may have guessed - is the line in red and we simply think of the left and bottom sides of the battlefield as axes of a graph (think of someone putting a massive ruler next to them) and also consider the friendly base to be the origin (point (0,0)). Now consider the production point to be the man and you now hopefully understand that the man (or production point) should probably be somewhere in the curved part of the graph. Note that if $x+y$ at the production possibilities frontier was constant then the red line would be a straight line (just equate it to a constant $c$, look: $x+y=c$, $y=-x+c$ i.e. a straight line with a negative gradient and y-intercept c$). You can consider the various values of producing different quantities of two different products (getting closer to any one base), taking into consideration the diminishing returns of production to alter the shape from simply being a straight line. The diminishing returns of production in economics are sometimes explained by the idea that resources being allocated to the production of one product would be more efficient if they were producing a different product. For example, if you focused all of a technology company's resources on producing software, the hardware engineers, who are better at producing hardware, would also work on software, but would produce less value to the company for each hour they worked on the software, compared to if they had been spending those hours working on what they were good, or efficient, at doing.