Past papers are ones that have been used in actual exams in previous years. They've got questions that students before you actually had to answer in an exam setting! The grades you study for and the exams set for them can change over time, but doing past papers is still a great way to prepare for the real thing.
The syllabus is the document that outlines all the essential information about the content of a specific grade. It lists the topics you will study, as well tests, quizzes, or exams. Your teachers should will give you a syllabus for each of your grades.