Your reservation isn't confirmed until you've added your payment information and the host accepts your request. If you've sent a reservation request to a host with Instant Book enabled, your request will be accepted automatically.
When a host accepts your request, you'll receive an email and, depending on your account notification settings, a text (SMS) and push notification from Airbnb. Your reservation request status will also change to Accepted.
To check your reservation status from your computer, click your name in the top-right corner of airbnb.com and select Dashboard. You'll find the status of current and previous reservation requests: