An External ID (also called XML ID) is a string identifier that uniquely identifies a particular record in Odoo.
They become important when you plan to import data into Odoo.
When you import data, if you supply an External ID, Odoo checks if this record already exists. If it does not, that line of your import file becomes an INSERT. If it does exist, that line of your import file becomes an UPDATE. If you don't supply an External ID (you leave it blank, or just don't supply the field at all), Odoo creates one automatically for you.
They are stored in the ir.model.data model and are not given to records that are created via the Odoo user interface - only for records that are imported (External ID is created or read on import) or exported (External ID is created on export if it doesn't exist already).
You can see the External ID for a record in Developer Mode using the View Metadata option in the Debug Menu.
When you export data, Odoo will ensure External ID's are present for every record in the export file, so you can update the file and import it back into Odoo (using the rules above).
The field is a char field composed two smaller char fields separated by a period character. The first part is normally the name of the module creating the record, or some other prefix. Both char fields can have up to 10,485,760 alpha-numeric characters in total, except the period character. You will run into usability issues before your run into storage issues. After 66 characters in total, the ID won't display properly on the screen and you will have to scroll your browser to see it.