Organisms may be less well adapted to the changing climate. The organisms will be outcompete by other organisms and it will be harder to them to find food and shelter which are crucial to the organisms survival. The organisms therefore will not be able to live for long enough to reproduce. This means that they will be less successful in passing on their genes to the next generation and eventually could become extinct if they stop reproducing altogether.
For example, if the climate in the Antarctic increases and the ice melts too much, then Antarctic penguins won't be able to survive long enough to lay eggs. If the penguins don't lay any eggs then they won't reproduce and the organism (penguin) will become extinct.