Bread rises because gas gets trapped inside the dough.
In many breads, yeast produces that gas.
The dough contains a stretchy network that holds the bubbles long enough for them to expand.
Put those two systems together and a small lump of dough can become a much larger loaf.
Yeast is alive
Baker’s yeast is a microorganism.
Given moisture, suitable warmth, and available sugars, yeast cells metabolize those sugars.
One of the products is carbon dioxide gas.
The yeast is not consciously inflating your bread.
It is carrying out ordinary metabolism.
The baker takes advantage of the exhaust.
What keeps the gas from escaping?
Wheat flour contains proteins that can form gluten when mixed with water and worked into dough.
Gluten creates a stretchy network.
Carbon dioxide bubbles become trapped in that network.
As more gas is produced, the bubbles expand and the dough grows.
Without enough structure, the gas would simply escape and the dough would not hold its shape well.
Does yeast eat only added sugar?
No.
Flour contains starch, and enzymes can break some of that starch into smaller sugars that yeast can use.
Added sugar can influence fermentation, but bread does not require a giant spoonful of table sugar for yeast to work.
Why does warmth help dough rise?
Chemical reactions and yeast metabolism generally proceed faster in a comfortable warm range than in a cold refrigerator.
That is why cold dough rises slowly.
Too much heat is different. High temperatures can damage or kill the yeast.
The goal is not “as hot as possible.”
It is “warm enough for the yeast to work.”
What happens in the oven?
When dough first enters a hot oven, gases expand and yeast activity can briefly accelerate.
The loaf may rise quickly during this early stage, sometimes called oven spring.
Then the temperature becomes too high for the yeast to survive.
By that point, proteins and starches are changing enough to set the bread’s internal structure.
The bubbles stop being temporary balloons and become the holes in the finished crumb.
Why do some breads rise without yeast?
Not every bread uses yeast.
Baking soda and baking powder can produce carbon dioxide through chemical reactions.
Steam can also expand and help lift certain baked goods.
Different recipes use different gas-making systems.
The principle is still similar.
Create gas.
Trap it long enough.
Set the structure before the gas disappears.
So a loaf of bread is not rising because the dough itself decided to become bigger.
It is basically an edible balloon system powered by microscopic fungi.
Which sounds less appetizing than “bread,” so we usually stick with bread.
A related bit of kitchen science appears in Why does popcorn pop?, where a different familiar food has its own chemistry.
And that’s the short explanation.
Related explanations: Why does popcorn pop?, Why does soda fizz?, and Why does swiss cheese have holes?