The economizing problem is the core problem of the study of economics. In fact, it is the reason we study economics - it gives the social science its purpose. Ok, enough of the bullshit, here's the economizing problem:
Even though the wants of individuals and groups are unlimited, economic resources are scarce.
Let's pick apart the problem. To an economist, there are no needs, only wants. A person 'wants' to survive, they don't 'need' to survive. So, they 'want' to have full stomachs, 'want' to have warm and adequate clothing, and 'want' to have shelter from the forces of nature. The fact that these wants are unlimited isn't too hard to imagine. You probably have lists of things you want to do, places you want to visit, gadgets you'd like to have, foods you want to eat, languages you want to learn, musical instruments you want to know how to use right - this goes on ad infinitum.
Every resource is scarce. The ultimate resource - time - is the most scarce. You can't save time for a situation when you really need it, it must be spent once its received. The other four specific resources - land, labor, capital, and entrepreneurial ability - are also scarce. There is only so much land, so many workers, so much investment money, so many ingenious people to go around.
In order to realize the best use of these scarce resoures, society must achieve both full employment - use of all resources, and full production - all employed resources are used so that they provide the maximum possible satisfaction of our material wants.
The great thing is that this can be graphed. It's called the production possibilities curve, and it shows the points of maximum output of two products (it's only two products because graphs in economics are only of perfect situations, and are used to illustrate principles. By using only two products, it simplifies the situation enough that one can see how allocative effieiency really works).
The economizing problem is what gives an
economist the fire in his belly.
Adam Smith, the 'father of economics' saw this wherever he went, and was amazed how an
economy tends to work out the problem rather well.