Think of something or someone that does not change as constant. A classmate's constant drumming on the table with his fingers could be a constant source of annoyance.
Constant derives from Latin verb meaning "to stand with," so something constant is continually standing with you and not wavering. You may be thankful for the constant companionship of your dog but not necessarily for your teacher's constant homework assignments. In math and science, a constant is a number that is fixed and known, unlike a variable which changes with the context. That idea crosses over to real life. If a friend is a constant in your life, that means they have always been with you and there for you.