What is the transfer of heat causing differences in air density?
Convectional currents, as, you already know, occur due to density differences.
A more accurate definition of convectional currents will be transfer of fluid from one region the other.
Convectional currents imply degrees of hotness and coldness a fluid possesses. Thus, a fluid which is less dense will rise upwards and therefore is hotter and another fluid which is denser will go down and therefore is colder.
One use of convectional currents will be heaters. Heaters are placed at the bottom of a room so as hot air to be able to rise upwards and colder air to go down. Its reverse effect are air-conditioners.