A Bachelor of Science degree is more technical than a Bachelor of Arts. To earn a B.A., you will not take as many math and science courses, and you generally have more flexibility in designing your curriculum. However, you may choose a career path that requires the more quantitative coursework involved in a B.S. If you are more interested in writing, art, or history, a B.A. is more your speed. Both degree programs require multidisciplinary coursework, so no matter your emphasis you will graduate with a well-rounded education.
Why do we call this program the bachelor's degree? The word "bachelor" was chosen because it means "young apprentice." After high school, the bachelor's degree is usually the first target. You can then choose to follow up your "apprenticeship" with a master's degree and doctorate. In some countries, and even in some American institutions, the bachelor's degree is referred to as the baccalaureate.
The most frequently awarded bachelor's degrees are the B.S. and B.A. There are other, more specialized bachelor's degrees also offered by some universities, depending on the field. For instance, an artist might earn a Bachelor of Fine Arts (BFA). An engineer might pursue a Bachelor of Engineering (BEng). A musician might earn a Bachelor of Music (BMus). Your institution may or may not offer these specializations.
A Bachelor of Science degree provides a solid foundation for a master's or PhD program in a related field. You don't have to pursue the exact same discipline for your undergraduate and graduate degree, but you will need to complete key prerequisite classes to earn admission into your desired graduate program. If you are interested in becoming a university professor or being the head of your own research lab, consider continuing your education beyond a B.S. degree.
Someone with a B.S. degree will be more limited in job responsibilities than someone with a higher-level degree. In most scientific fields, B.S. holders work mainly at the technician level. They are also paid less than those with higher degrees. However, if you do not want to go to graduate school, you can also earn work-related skills through internships while you're still in college. Internships might give you an advantage in finding a job after you graduate, because you have the skills that your competition doesn't have.