Most likely, yellow leaves appearing on your Begonia is caused by overwatering, allowing soil to stay soggy, or letting the plant sit in water. This is an easy fix, going forward. When you water, water thoroughly until water comes out of the drainage hole. Wait a few minutes until it drains, and then empty any water that has accumulated in the saucer. Allow the soil to dry about halfway, or 2-4 inches down before watering again. If the soil is kept too wet for too long, the roots may rot.
Making sure that the plant is getting enough light will help reduce overwatering symptoms. If your Begonia is in a lower light situation, it will take longer to use water and can lead to overwatering symptoms such as yellow leaves. Moving your Begonia closer to a window can help improve the health of your plant.