This isn't a very thorough explanation.

The greenhouse effect of certain gases, including carbon dioxide released from burning most flammable substances, increases as the gasses accumulate in the atmosphere.

Carbon dioxide, at current levels, is bad. As the air retains more heat, it also holds onto water more, which is a much more potent greenhouse gas - which accelerates the warming.

The air then can hold more water. This reaches a point where no more will be held, but it's bad for most animal life. Plant life usually doesn't mind.

With the planet getting warmer, other things start happening. The polar ice caps melt and cause the oceans to rise, flooding coastal areas. The warm air also has more energy (that's why it's warm), making it go faster - hurricanes, tornados, that sort of thing get worse and more common.

The weather completely changes so we have trouble knowing from history where all the rain will go - causing areas that normally don't flood to flood, and lakes to go dry.

The ocean also warms up. This has a really negative effect on ocean life. Lots of it dies because they're evolved to live in cold water. Evolution requires a bit of time to adjust, so it's a mass extinction.

Things that can survive the change in temperature can't survive the loss of their food. Much of our breathable oxygen comes from plants in the ocean, which also die.

The warm water can hold carbon dioxide better, which offsets the stuff in the air to a point, but this acidifies the ocean, killing even more things, like reefs. More plants die. More animals die.

All of this is happening right now, within our lifetime, which means evolution will largely fail to accommodate our food. We die.

Then it all goes back to normal over the next few thousand to million years, new species rise and take all the unoccupied niches.