If you omit one member of the class when you're handing out valentines, it's going to make that person feel terrible. To omit something is to leave it out, to forget or overlook it.
The verb omit comes from the Latin word omittere, "to let go or to lay aside," which is exactly what it means. When you omit an ingredient you need for your brownie recipe from the grocery list, you've accidentally left off an important item. You can also deliberately omit something, which you'd do if you didn't include your least favorite cousin when you invited your relatives to a family reunion.