Compulsory classes are the ones you must take in order to get your degree. Some colleges may give a choice between two similar classes for some compulsories, but in general compulsory classes are quite specific and can't be substituted, except by an equal transfer class from another college. Compulsory classes are called other names as well, such as core classes or major-specific classes.
Mostly considered fun classes, electives are those where students have the most choice. Most colleges provide a degree plan for each major specifying compulsory classes and leaving room for electives, classes you can take just because you find them interesting and they're not already compulsory. Study your degree plan carefully before deciding, though. Some schools ask that at least a few of your electives lie in specific areas, such as technology, art or music.
Prerequisites are classes which must be taken before you can enroll in another class, usually the same but at higher level. For example, most students have the take a beginner's level semester of a foreign language before they can move up to the higher ones, or Introduction to Computer Science before they can begin programming classes. However, most nursing schools require an entire array of prerequisite courses before students can even be admitted in the first place, such as anatomy, microbiology, nutrition, chemistry and psychology.
Lecture classes are those in which there is almost no interaction between the teacher and the students, except for the occasional question. These are often core classes that almost every student must take, located in large halls. Students listen and take notes while the professor presents the material; there are often no grades or assignments other than tests, mid-term and final exams.
Lab classes usually accompany science or technology classes. They're hands-on classes, where students get out of the lecture hall and actually use what they are learning in a controlled setting. Computer and foreign language courses also may have labs, where students must spend a certain amount of time using certain programs, watching or listening to authentic materials and taking quizzes.