What is an Assignment and how does it relate to a Gradebook?

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I am new to using Assignments and am sorry if this is a simple question. Can someone please explain to me exactly what an assignment would be used for and how it relates to a gradebook? I assume it's to assign an ILT or a course directly to someone. It's very difficult to figure out functionality by just poking around or reading the online help materials. They're really not that clear. Also, in looking at some of the other threads, it seems that you used to not be able to force a completion status on those assignments. Is that still