In a helpdesk, a contact is a customer or a potential customer who has raised a support ticket through any channel. When there is a customer facing helpdesk where contacts can check their ticket statuses, a contact will be asked to activate their account and create a password.
Companies who want to track and understand the activities of the customers import the contact list from their CRM systems into their helpdesks. They also make sure that their CRM systems and their helpdesks are tightly integrated, so that any information changed in either one of these are updated in both. This helps sales and support teams get the entire context everytime they talk to a customer.
If multiple people from the same company contact the helpdesk, they can be grouped into a 'company'. Contacts can be tagged based on their behavior, business value or the amount of hand-holding they need.