what is the use of Baking soda in baking?

As others have mentioned, baking soda is a leavening agent. Baking soda reacts with anything acidic (like vinegar, molasses, buttermilk, etc) to produce carbon dioxide bubbles which expand when heated and give baked/fried goods their rise.

Secondarily, baking soda helps with browning.

Well, the bubbles that CV references make the dough rise, and then with heat the dough stiffens and those bubbles create the crumb. Much like yeast does for yeast bread, that is what it is called leavening, it causes the rise so that a baked product is usually higher than the level of the wet dough.

I think it also has something to do with expanding the dough.

Primary use: leavening agent.

It reacts with other components in a mixture to create carbon dioxide which forms bubbles in a batter. This characteristic is prized in baked and fried goods.