Yes, colleges generally have semester systems, where you take certain classes in Fall (August - December) and Spring (January - May). Some schools have trimester systems, such as many UC schools, with Fall (September - December), Winter (January-March) and Spring (April - June). Both systems have a summer school session too.
Most schools only allow you to apply for the Fall semester because that is when school starts, but some schools allow you to apply for the later Winter/Spring semesters and start later than most students. This is because some students will drop out after their first few months, leaving openings.
Hope that helps.