Core classes are usually referred to as general education requirements, and all students need to complete the necessary courses to graduate. For instance, even if you're a computer major, you'll still need to take a certain number of English classes, foreign language classes, history classes and others. The purpose of core credits is to make sure that every student who graduates from college has basic knowledge and skill sets. On the other side though, many of these classes are extremely similar to those that college students took when they were in high school.
While it's not required for all majors or at all colleges, a thesis is often considered the capstone of your college major. Your thesis is a paper that represents your attempt to research something directly related to your major that you feel strongly about and explaining the results to those in your department. A thesis paper is sort of the final test that students go through to show that they learned how to conduct research, how to write their findings, and how to actually answer questions through using the knowledge they've gained during their college years.
In order to graduate from college, students will also have to take a number of elective credits. These classes can be practically anything; what they do is allow students to pursue their own interests and desires. For instance, an English major could take creative writing as part of her degree, but a geology major could take creative writing as an elective because he's interested in the class. Electives represent the idea of a well-rounded education and make sure that students are exposed to a variety of different ideas and subjects.