If you are creating a Customer / Vendor using something like this:

new_customer_vals = {
 'name': customer_name,
 'company_type': 'company',
 ...
}
new_partner_id = sock.execute(dbname, uid, pwd, 'res.partner', 'create', new_customer_vals)

Then you can create the External ID immediately after you create the Partner record using something like this:

new_external_id_vals = {
 'model': 'res.partner',
 'module': 'api_generated',
 'name': unique_customer_ref,
 'res_id': new_partner_id,
}
it_worked = sock.execute(dbname, uid, pwd, 'ir.model.data', 'create', new_external_id_vals)

When you create invoices using a partner external_id that external_id needs to be created.

When you import something you can provide Odoo with and external_id or Odoo can generate it for you. External ID is a reference that you and Odoo agree to used to reference an object. Odoo external id's used for import are ephemeral but they allow you to name your imported partner so that you refer them next time you import. Other option is to use the Database ID which is the existing id of the partner on the Odoo database (once created never changes).