Points on graph, some coloured in, some not - what do they mean?

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We are dealing with limits and I don't know what terms to search for to find out what the full circle and 'hollow' circles on points on a graph represent. Can someone please fill me in.

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A hollow circle means a discontinuity caused by a specific point being taken off the graph. It could mean a removable discontinuity, or it could mean that the interval is open instead of closed. Wikipedia has a nice article partially explaining this topic, do take a look.

On the other hand, a full circle is a point defined on the graph (hence the function), and could signify that the interval is closed at that point.