What is a 410 Gone HTTP response?
A 410 HTTP response should be used when a resource is no longer found at a specific URL and will not return (it will permanently not be found).
What type of HTTP status is a 410?
A 410 is in the 4xx class of status codes which are client error based.
When should a 410 response be used?
A 410 status code should be used when a resource will never be found again.
For example if you have a product on your website that you are 100% sure that you will never get in stock again and don't want to sell anything similar, you might decide to use a 410.
410 vs 404 which is better for SEO?
If you know for sure that a resource will never exist again - a 410 status is potentially a little better for SEO.
If there is a chance that the resource or product may become available again at some date in the future then it would be better to use a 404 status.
Does a 410 HTTP status affect SEO?
A 410 status code does have a specific impact on your SEO, in that it provides a clear signal to search engines that they don't need to return to a resource again in the future.
Overall though it isn't worth getting obsessed over if you can use a 404 that will be fine in most circumstances.
The 410 (Gone) status code indicates that access to the target resource is no longer available at the origin server and that this condition is likely to be permanent. If the origin server does not know, or has no facility to determine, whether or not the condition is permanent, the status code 404 (Not Found) ought to be used instead. The 410 response is primarily intended to assist the task of web maintenance by notifying the recipient that the resource is intentionally unavailable and that the server owners desire that remote links to that resource be removed. Such an event is common for limited-time, promotional services and for resources belonging to individuals no longer associated with the origin server's site. It is not necessary to mark all permanently unavailable resources as "gone" or to keep the mark for any length of time -- that is left to the discretion of the server owner. A 410 response is cacheable by default; i.e., unless otherwise indicated by the method definition or explicit cache controls (see Section 4.2.2 of [RFC7234]).
Hypertext Transfer Protocol (HTTP/1.1): Semantics and Content