When purchasing a gun through an official gun dealer it is required to complete a ATF form 4473. It contains basic information and screening questions to determine if a buyer is eligible for gun ownership. Generally, buyers are either approved or denied. Denials can be due to criminal convictions but surprisingly, the majority are denied due to non-U.S. citizenship.

The third result is somewhat different. It is possible to get a conditional approval. While the conditional status does not always result in approval, the process and reasoning is somewhat interesting.

The background checks are conducted using NICS. The National Instant Criminal System is searched by name, location, and DOB. You may optionally provide a social security number, but the majority of searches are run without them. If you have a common last name (John Smith, Tom Jones, etc) you may be granted a conditional status because of hits on other individuals with the same name.

Here is why I called it a "conditional approval." You will not be able to take possession of the firearm for up to 5 days. If the NICS does not come back with an approval or denial before the 5 days, it's automatically approved on the 5th day.