In this example, "the table" can be understood as "the company at the table". So she is either quite pretty, or good conversation, or both. A non-human "nice addition to the table" would be a flower arrangement or a conversation piece (an interesting ornament). Anything that improves the general feeling of sitting at the table.

If someone were seated at a family's dinner table, perhaps expected to be on a regular basis for whatever reason, then this kind of a compliment could be rendered.

Well, I'll have a guess. If she was the one that has set the dinner table for example, then it means that she added something creative, a bunch of flowers for example! But if she was invited, then they might have meant that her presence or attendance was a nice addition to the meeting.