Drinking more water does make you more regular in your bowel movements.
One of the causes of constipation is dehydration and not enough water intake so increase your water intake can help keep your colon hydrated as well and prevent constipation and make your bowel movements more easier to move as well.
When you keep your body and colon properly hydrated it means that less water will be withdrawn from your colon which prevents constipation and keeps you more regular.