Low interest rates can be a very useful tool in stimulating economic growth. The main principle is that low interest rates help make money more readily available for people and businesses to use on various goods and services.
From a consumer level, lower interest rates can help with increased home, automobile, and other costly purchases by allowing more money to be spent on the product and less on the interest rates. Lower interest rates can make monthly payments on homes, cars, or appliances plummet by hundreds of dollars a month. It also might allow a person to qualify for a loan that might otherwise not be able to due to their economic status. This stimulates businesses that sell these goods and keeps the employees of those businesses with plenty of work. In turn, those employees will have the money to spend in what many economist refer to as the "multiplier effect".
At a higher level, lower interest rates allow businesses both large and small to have access to low interest cash to invest in their businesses. This could come in the form of infrastructure, employees, or inventory. Low interest rates could cause a farmer to decide to purchase an upgraded tractor, a small business to hire another employee, or a commercial giant to expand to another city. Each of these scenarios improve the economy by adding more jobs to an area or providing new contracts for services.
While there are some potential pitfalls to lowering interest rates, it can have an immensely positive impact on a country's economy.