Global warming refers to the anthropogenic warming of the planet. This warming comes from intensifying the greenhouse effect, an effect that exists on many other planets and has existed on Earth for almost as long as the planet has. When used in conversation, climate change and global warming are sometimes used interchangeably, as there's no difference. It is more accurate to say that global warming is one of the many signs of climate change.
The planet is certainly warmer than it would be without the greenhouse effect, see here for details. The temperature of the Earth has been going up in recent decades (see figure 1), and this warming will cause an increasing number of problems for people around the world in the decades to come.
Global warming is only one of many problems caused by climate change. At the moment, many of the consequences of global warming have been relatively benign, and sometimes even beneficial, but as global warming intensifies the consequences will keep getting worse.
Global warming is:
Humans use energy to maintain a high energy society that provides a good quality of life. This means the amount of energy that people use keeps increasing (see the pages on the BRIC and N11 countries for great examples of this). Unfortunately, most of the world's primary energy comes from fossil fuels, which is why climate change is so hard to stop.
There are lots of fossil fuels left. In fact, the biggest problem the world is facing isn't that fossil fuels are going to run out! We have enough to continue burning these fuels for decades to come. However, it will continue to induce problematic global warming, and climate change in general.