Protectionism refers to policies that provide economic sanctions that protect specific markets within a country against outside competition. Common examples are tariffs on foreign goods and subsidies to local producers.
Protectionist policies hamper the functioning of the free market, which most economists consider to be a Bad Thing. To give an entirely hypothetical example, if Japan can make cars better and cheaper than Americans can, then it would be silly to use up talented Americans making expensive or shoddy cars when they could be doing something more productive with their time. The free market would redirect these American workers to jobs in which they had a higher comparative advantage, and we would all, Americans and Japanese, be a little better off. (In theory.)
There are many reasons for protectionist policies. One big reason, especially in America, seems to be that we fear that there is nothing that we can reliably do better than a foreigner can. We don't want free international trade because we don't believe that we would be a top producer, which would put us behind in the world market. The theory of comparative advantage suggests that this fear is unfounded, and more importantly, even if we shore up internal markets, that won't help our standing in the world market.
Another reason for protectionism is a general dislike of change. Those working in the auto industry (and all those service industries built up around cities like Detroit, that depend on the auto industry) do not look forward to the major life changes that would be necessary if the American auto industry were to collapse. Many would be worse off, and all would suffer from the burden of changing jobs, having to move their families, and learning new skills, all of which have both monetary and psychological costs. Hence, many workers belong to unions that lobby for protectionist policies protecting their industry.
It is important to remember that all forms of protectionism come with their own costs. Subsidies are paid for with the taxes that we all pay. While one group comes out ahead, fellow countrymen have to pay the price. Tariffs are present another sort of cost. When those who are importing goods have to pay a fee, that cost is passed on to the consumer. This means that he has to pay the tariff. Of course, he doesn't have to pay the tariff; he could simply buy the locally produced goods. But if he needs to be threatened with the additional cost of the tariff to make the locally priced goods worth buying, this means that he is being coerced into living with second rate goods, at a cost higher than the free market would have set.
There is at least one very good reason for protectionist policies. Politically, countries realize that it is a Bad Thing to be dependent on another country for the majority of your food, or steel production, or energy needs, or any other product that is necessary to smooth functioning of the economy. Most countries provide subsidies to industries that they feel are crucial to the nation's functioning in case of war or other international crises. Self sufficiency is still seen as a major issue by most countries, and not without some reason.
As you might have guessed from the above writeup, I'm mostly against protectionism, and mostly for free trade. But these are very complex issues, and I'm only writing a very simple introduction. Any sort of policy can be abused or misapplied, and there are good reasons to protect some industries (I'm all for government subsidies to emerging markets that provide efficient new energy sources). If this stuff sounds interesting to you, read more, and then write to your congressman. (Or member of parliament. Or you know, whoever.) These are exactly the sort of world-changing policies that are left almost entirely up to politicians and the special interest groups that lobby to them. They need your input!