In economics, opportunity cost is value that you cannot consume because it is not possible to consume all alternatives.
This is often misunderstood, as opportunity costs only include the difference in value that is forgone, not the entire value. For example:
I need to eat breakfast. Sadly, I only have room in my stomach for one breakfast. I look at my options and see that I can buy pancakes for $5 or waffles for $5. I love both, and value them at $8 each. I'm getting a great deal either way, but I choose pancakes. If opportunity were not limited, I would buy both... but I can't. Opportunity cost is $3, the additional value that I was offered (in the form of delicious waffles), but that I could not take advantage of.
I need to eat lunch. Sadly, I only have room in my stomach for one lunch. I look at my options, and see that I can eat a bowl of oatmeal for $1, or steak for $10. As it happens, I don't much care for oatmeal, but it will fill me up, and I think that the oatmeal is indeed worth $1. I do like steak, and value it ten times as much as I do oatmeal. But... this means that both the oatmeal and the steak are priced at exactly the correct value. It doesn't matter which I eat, there is no opportunity cost. (If I choose oatmeal, any sadness that I feel at forgoing steak is exactly offset at the joy I feel at having those extra nine dollars in my pocket).
I need to eat supper. Sadly, I only have room in my stomach for one supper. I look at my options, and see that I could have pizza for $10, or calzone for $10. I like pizza more than calzone; I value a pizza at $12, but a calzone at only $8. If I chose the calzone (why?!), the opportunity cost would be $4 -- the $2 I spent above my perceived value of the calzone, and the $2 worth of value that I would have gained in enjoyment of the pizza.
Of course, usually opportunity cost isn't limited by stomach capacity. My breakfast conundrum could just as easily be caused by lack of funds; if I had only $5 in my pocket, then I would still have to make a choice with an opportunity cost of $3. Opportunity is also often limited by time (e.g., I only have 15 minutes to eat).
Unfortunately, most examples are much more complex than meal choices, and the opportunity cost of going to college vs. starting work four years earlier is not calculable in precise terms -- you would have to know exactly what career path you would follow, including how quickly you can be hired under each scenario, how much you will earn at each job, how often you change jobs, health risks and costs associated with each job, and extra-monetary concerns like stress and quality of work environment. However, we usually have ample information to determine which course to follow, even using vague intuitions of possible opportunities and costs, in large part because many of the values we are balancing are not monetary, but social or emotional.
Perhaps the most clear-cut cases of opportunity cost is in financial investment, where one can track both the results of one's investments and the outcomes of alternative investments one could have made. While this is interesting in helping provide a post-mortem of your finances, it doesn't provide much guidance for future investments, as the central question of planning investments is how much risk you are willing to tolerate, with the greatest potential rewards coming from those investments where opportunity cost is least calculable.