How does the metaphor of the commons explain the global ecological situation?

Well, the idea is that, with common land, you get whatever you can out of it, because if you don't someone else will. If you decided "I'm not going to exploit this land, as that will ruin it" someone else will exploit it. On the other hand, if each of you owns a particular section of the land, then no one else can exploit your bit. The metaphor of the commons is commonly used by advocates of private ownership (ie opponents of socialism and communism).
This applies to the global ecology as well. A good example is European cod fishing rights. Cod has been over-fished, and is running out. Now, the metaphor of the commons says this: if anyone can fish, then everyone will think "I better get all the cod and sell them. After all, if I don't, someone else will fish them and they'll all be gone anyway." So all the fishermen would try and fish all the cod, even though they'd know they were destroying their own livelihood. If, on the other hand, one group has a monopoly over all cod fishing, then they will fish at sustainable levels, in order to keep selling cod without wiping out cod.

In fact, the EU doesn't use either system, commons or private ownership. It uses a quota system, where anyone can fish but they can only get a certain amount. I don't know exactly how it works though.

Another example is global warming. The atmosphere is common to all of us. Many people say that we should not pollute it with CO2 as it will cause global warming. But the problem is, if say America stops producing CO2, China will still be pumping out loads, and so global warming (assuming it's real) will happen anyway, and affect America as much as China. So there is not much point in America reducing CO2 levels. So it doesn't. But then China has no reason to reduce it's CO2 levels either, because they will suffer from global warming caused by American pollution. So in the end, no one does anything, and global warming happens.

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... I am surprised at your insolence in writing to me at all. You know, as I know, that I bought this constituency... may God's curse light upon you and may it make your women as open and as free to the excise officers as your wives and daughters have always been to me while I have represented your scoundrel corporation.
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Quite simple reaaly, there is a set amount that people can catch, you can't catch females and males have to be under a certain size. They check how many are caught and all that.

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I see, thanks.

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... I am surprised at your insolence in writing to me at all. You know, as I know, that I bought this constituency... may God's curse light upon you and may it make your women as open and as free to the excise officers as your wives and daughters have always been to me while I have represented your scoundrel corporation.
I have the honour to be... your obliged humble servant, Anthony Henley
- MPs reply to constituent, mid 1700s

The "commons" is a term for lands or resources belonging to all, i.e. "held in common." Navigable waters (large lakes, streams, ocean) supposedly cannot be privately owned. Theoretically, they are the property of all and are supposed to be managed for the benefit of all citizens. National forests, national parks, wildlife refuges, and other federally owned lands are supposed to be managed for the common good of all U.S. citizens, including future generations. Unfortunately, that ideal is not always realized.

One of the problems with the commons is the tendency of some to excessively exploit them for narrow, short term private gain or to abuse them, because they disrespect commonally held values. Historic examples include the fouling of the air and water, degredation of wildlife habitat, the over harvest or even extinction of native plants and animals, etc.