A contact is someone that has given you their email address. This might be through the chat, forms, chat bots, meetings, etc. Their entire history is then saved inside Gist.
If you are on the Free or Support plan, you get unlimited contacts that you can continue to track and converse with through chat. However, you are NOT able to send them emails at all after you reach 500 contacts. The Growth and All-in-One plans are billed based on the number of contacts in your account as those plans give you the ability to send emails to all your contacts.