How do convection currents transfer heat in the atmosphere?
It moves it upward.
According to Charles's Law, temperature and volume are directly proportional, but according to Boyle's law volume and pressure are inversely proportional. In the case of convection, volume is not constant. That is to say an air mass near the surface of the Earth can expand when it is heated. This occurs because in the case of convection, the Earth is unevenly heated. The air that becomes warmer can expand into the areas where the air does not become as warm.
Since we just established that the warmed air can expand we also know that the pressure inside that air will drop as the volume increases. With lower pressure inside the air it will start to rise. Since this air is warmer, it is a vertical transfer of heat.
The majority of the time, with convection we have latent heat transfer as well. If you would like to know about that please let me know.