The appraiser's role in the home buying process is to determine a value of the property for their client, the lender.
No, not for you, the buyer, but the appraiser is looking out for the lender's interests in the value of the property, because if something goes wrong and you can't make the payments any longer, then the lender needs to know that they have a salable property.
In the early 2000s, it was easier for appraisers to value properties, because home values kept rising. Though they did need to be careful not to over-value. Now, appraisers need to figure out if an area is rising, stable or declining in value.
Appraisers have guidelines they need to follow to provide lenders with an accurate picture of the property and in the current marketplace of increased foreclosures and short sales, appraisers are being required to follow more stringent guidelines.
If the appraiser determines that there are repair, defect or improvement issues attached to the property, they may need to be addressed by the owner or buyer of the property before a sale can be completed.
It's extremely rare that you'd ever see or talk with an appraiser. They are expected to give an un-biased, third-party opinion as to the value of the property. Now in the event the appraised value of the property comes in below the agreed-upon sale price, then your agent may be able to offer information about other sales that could make a difference in the final outcome of the appraisal, but normally it won't sway the appraiser, because they have access to the same information as most agents and they do a lot of research too.
So when you're ready to make an offer on a property, understand that the lender's appraiser doesn't come into the picture until after you have an accepted agreement with the seller. Prior to writing your offer, you need to have your buyer's agent prepare a C.M.A. (Comparable Market Analysis), that will show you where values of comparable properties normally within a one mile radius have been in the last 6 - 12 months. That should help you select an asking price based on those recent sales as well as the condition, location and motivation of the seller.
If you're looking at a 3 bedroom ranch home on a slab with a 1-car garage, then you shouldn't be comparing that to 3 & 4 bedroom 2-story homes with full basements & 2-car garages in the same neighborhood. You need to find homes that are as closely similar to yours as possible.
Also, If you want to buy a condominium, the appraiser and lender may also want to review the condo documents as well.
I hope this sheds some light on the role of an appraiser.