-----------------Updated June 2017--------------------
An updated version of this Community Guide is now available, click here to view.
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I see several hosts wondering why their response rating has decreased when they have responded to all their inquiries and requests. It is important to know the difference between a “reservation inquiry” and a “reservation request” and how not responding to one can affect your response rating.
All About Reservation Inquiries
First of all, Airbnb suggests that guests send out several reservation inquiries when looking for a place to stay using Airbnb. When a guest sends an inquiry, they usually send them out to several listings in the same area. It is kind of like window shopping for an Airbnb listing. The guest can screen hosts by sending a question (inquiry) but they need to complete the dates which they are inquiring about staying and the number of guests. A guest may receive pre-approvals from several hosts enabling them to choose which listing fits their needs best. The important thing to note on "inquiries" is that all you have to do is "respond" to the inquiry within the 24 hours to maintain your response rating. It is of course best to screen the guest who is inquiring and either "pre-approving" them or "declining" them but the most important thing is to at least respond to them within the 24 hour time frame.
How Does a Guest Make an Inquiry?
For the guest to make an inquiry, they will choose your listing and then choose “Contact Host”.

A box will then pop up where the guest can enter the dates they are inquiring about, the number of guests, and their message and questions for the host. They then send the inquiry.

What Does the Host Receive When a Guest Sends an Inquiry?
The host will then receive the guest’s reservation inquiry and have the options to either “Pre-Approve”, “Decline”, “Respond”, or “Dismiss”. All you really need to do is “Respond” to the inquiry within 24 hours of receiving it and your response rating will not be affected. If you “Pre-Approve”, you are essentially allowing the guest to Instant Book the reservation. If they choose to go with your listing after you pre-approved them, they will complete the checkout process and your listing will be booked for the dates you pre-approved for. You also have the option of sending a "Special Offer".

or

If you choose to just respond, you will converse back and forth through the messaging system.

This is what the guest will receive in the messaging center if the inquiry is "pre-approved".

All About Reservation Requests
It is essential that you understand "reservation requests". A reservation request means that a guest is ready to book your place and they just need your approval. Once you approve their request, your place will become a confirmed booking. It is also important to know that you have 24 hours to take action on the request by either "accepting" or "declining" the reservation request. If you do not either accept or decline within the 24 hours, your response rating will be affected. So, if you have a guest who is taking their time getting back to any of your questions and the 24 hour clock is running down and you are not quite comfortable yet with the guest, it is best to decline the request. You can explain to the guest that you are declining their request because you would like more information and that they can make another request.
How Does a Guest Make a Reservation Request?
For a guest to make a request, from your listing, they would choose the dates, the number of guests and then choose the "Request to Book" tab.

The guest would then be taken to the payment screen.

The guest would then fill in the "About Your Trip" section where the House Rules are stated, they can confirm or add the number of guests, and agree to the House Rules, Cancellation Policy and the Guest Refund Policy.

Finally, the guest can add the names of the additional guests and their emails and also have the option of having the itinerary emailed to anyone.

What Does the Host Receive with a Reservation Request?
The host will receive the reservation request notification. When they click on this, they can either "Approve", "Decline", or "Respond". The host will only have 24 hours to take the action of approving or declining or their reposnse rating will be affected.

If the host chooses to "Accept", the reservation is booked and confirmed. If you wish to decline the reservation, you will be taken to a screen where you choose the reason for declining. You also have the option to explain why you are declining the request. If you wish to provide a message to the guest, you can do this as well.

Thank you so much to @Clare for helping me out with creating this Help Guide. You rock!