Here's the ArcGIS help section on metadata. Read some of this http://resources.arcgis.com/en/help/main/10.1/#/What_is_metadata/003t00000001000000/
If you have access to ArcCatalog, you can then take a look at the metadata that is generated by default for a spatial dataset. Highlight a spatial dataset (like a shapefile or layer in fgdb), hit the Description tab, you'll see a description of data and thumbnail. Then go to Customize > ArcCatalog Options > Metadata > Metadata Style, change to use the newer "North American Profile ISO 19115 2003" style, hit okay. Click out of Description tab and back into it, and you'll see a whole bunch of fields for that standard. You could then edit those -- it is likely someone may want you to fill these in with information for your internship.
Behind the scenes, ArcCatalog saves metadata as an XML file when using a shapefile or inserts it as a long XML string into a database (like a layer in a fgdb). XML has a dtd or xsd that validates the structure of the XML (e.g. whether an element is mandatory or can occur multiple times, etc.) ArcCatalog or other tools will use a xsd/dtd to validate the metadata based on the chosen metadata style.
Here's some information on the older FGDC (CSDGM) format (which is still used quite a bit) and the ISO 19115/19115 NAP/19139 -- the ISO ones are essentially the same thing. And they all (including FGDC) use XML for structure and validation.