Yeast cells reproduce very rapidly no matter where they are. This reproduction goes on through a process called budding. In budding, each tiny cell swells, and soon the swollen part separates from the main cell. The new tiny cell then goes on to grow to full size on its own and the budding process continues to repeat itself.
During this growth process, the yeast cells produce substances called enzymes. So when the yeast is added to cake or bread dough, one enzyme goes to work on the flour, changing the starch in it into sugar.
Another enzyme then takes over and changes the sugar into alcohol and a gas called carbon dioxide. This gas spreads through the dough in the form of bubbles.
As the dough bakes into bread and cake, the heat causes the alcohol to evaporate and the bubbles to break. This leaves the tiny air pockets in the final bread or cake, making it light and fluffy.
Before yeast was manufactured commercially, women did their baking by mixing flour, salt, sugar, and potato water, and letting yeast cells in the air supply the enzymes!