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Metadata is, simply put, data about data.
Let's say we have this data; "Alexander." We have really no way of telling what it is, but people who have heard the name Alexander before will recognize it as such. A computer doesn't really know, nor doesn't care most of the time, about what "Alexander" means. That is why we provide some data about the data; "First name". Putting these two bits of data together makes sense.
Metadata is data about data as shown in the "metadata" box in the right-hand column of this page. Typical metadata is title, date, comments and author, but more advanced metadata is links, relations and occurences of a given metadata, such as shown in the "see also" link also in the right-hand column.
There are many ways of creating data about data. You can have almost a limitless amount of levels of it, too, like metametametadata, and so forth.