SEO stands for "Search Engine Optimization". It is the process of optimizing a website, or content to display on a search engine result page or "SERP".
SEO - or Search Engine Optimization, is an art and a science. It starts with accurate keyword research - identifying keywords or search terms that relate to a website, and then optimizing a web page or website to answer the question the searcher originally wanted to know about by typing it into a search engine.
SEO is important because it puts the searcher first. SEO helps search engines connect a specific search term, with a list of relevant results in a search engine results page. Without doing SEO (properly), a site owner would just be guess work as to who is searching for their products or services.
Yes, as soon as people stop using search engines, which may be never, so on second thoughts, no, never. As long as people are using search engines to answer questions, SEO will be there to help websites craft answers to them.
A Search Engine Results Page, or "SERP", is a page of search results that search engines have determined are relevant to the original search input by the searcher. The process of Search Engine Optimization is an attempt to identify what search results are relevant to a product or service or news article you produce, and then creating it, making it as accessible to search engines as possible to index, and then optimizing content for how users interact with it.