To delete a contact:
The contacts that you see in WhatsApp come from your iPhone's Contacts app. Please note that when you delete a contact from WhatsApp, this will also delete the contact from your iPhone's Contacts app.
Deleting a contact from your Contacts app will not delete any chat history you have with that contact. Learn how to delete a chat from this FAQ: How do I delete messages or chats?
Learn how to delete a contact on: Android | Windows Phone | Nokia S40 | BlackBerry | Nokia S60 | BlackBerry 10
Cheers,
WhatsApp Support Team