The production possibility frontier, usually abbreviated PPF, is used to describe the production capacity of a country, or in some cases an individual business.
Usually we draw it in two dimensions for convenience, though in reality it should have many dimensions, one for each product that could be produced.
Along the PPF, production capacity is fully utilized; it is not possible with current resources and technology to produce any more. We can move along the PPF in each direction, producing more of one good and less of another good.
We can also move inside the PPF, producing less of both goods; but this would mean wasting our productive capacity, because we are capable of producing more than we are actually producing.
The one thing we cannot do is move outside the PPF, producing more of both goods; outside the PPF is a level of production we simply can't achieve. We'd like to if we could, but right now we can't.
The PPF is extremely important in describing a range of economic phenomena.
The PPF can be used to explain the concept of opportunity cost: Rather than measuring costs in dollars which are rather arbitrary (and change with inflation), we can measure the cost of producing one good in terms of not producing other goods. As you move along the PPF to produce more X at the expense of less Y, the opportunity cost of X in terms of Y is the slope dY/dX.
The PPF is often applied to international trade: Because different countries have PPFs of different shapes, they can trade with one another to produce more efficiently than either country could do alone, thus effectively expanding their consumption beyond their individual PPF. (Put another way, the combined PPF of both countries is larger than the PPF of each country alone.)
The PPF can also be used to describe inefficiency in production, unemployment, and the business cycle. During a recession, the economy is producing below potential GDP because people are unemployed. This means that we are below the PPF and could have more economic output if we employed everyone and produced at full capacity.
Finally, the PPF can also describe changes in technology and overall economic growth. If technology makes production of one good more efficient, the PPF will expand in the direction of that good. If there is growth in the economy as a whole, the entire PPF will expand outward.