Metadata is data about data. Metadata can often be thought of as a label on some bit of information that can be useful to people or computer programs trying to use the data. Without metadata, the person or computer trying to use the original information would have to guess what the original data is about.
When resources are published at least title, subject and keywords should be provided so that the resource could be found easily.
For example, if you create a problem and neglect to say in the title or subject of the problem what it is about, then a human who wants to use that problem would have to read the problem itself to see what it was about. This is much more difficult than just reading a title. A computer trying to do the same thing would be out of luck; it is too stupid to understand the problem statement at all.
Another example of metadata is the < title > tag of a web page, which usually shows up in the title bar of the browser. That is information about the web page itself and is not actually part of the web page. People use the title information when they bookmark a page. Search engines use it as a clue about the content of the web page.