In the world of financial markets, the "carbon bubble" is the notion that companies around the world involved in drilling, refining, and marketing fossil fuels are currently dramatically overvalued by financial markets, because their sky-high valuations are based on vast proven and expected reserves that will never be drilled or burned due to our growing understanding of anthropogenic global warming. Proponents of the carbon bubble idea argue that sooner or later, this financial bubble will pop, leading to a crash in the valuations of these companies - either sooner because governments around the world preemptively place caps or other limits on carbon, or else later as the devastating effects of global warming caused by unrestricted fossil fuel burning give nations no choice but to drastically curtail consumption.
In recent years, increasing demand for fossil fuels, especially from China and other developing markets, has made fossil fuel companies fantastically profitable, and has driven their valuations on stock markets extremely high, but if there really is a carbon bubble, at some point investors are going to want to start divesting themselves of the stock of these companies. As of right now, these companies remain ridiculously profitable, and their stock prices keep going up and up, so it's tempting to stay invested in them as long as possible. The trick is knowing when to get out.