WhatsApp has an optional auto-backup feature that periodically backs up your messages to Google Drive (iCloud on iOS?). You can find it under Settings > Chats > Chat backup. It is an extremely smart way to allow users to backup their messages if needed, while also ensuring that WhatsApp doesn't have access to the backups.

Once you activate a new phone, it will ask if you want to restore your messages from the latest backup. I guess it's using your Play Store account credentials to tie your SIM cards and phones together.