Search Engine submission is the means by which you can tell a search engine that your webpage / website exists and to please go and crawl the site. Here is the Google URL Submission page and Bing's submission page. In days gone by Search Engine submission was useful for new websites to give a little wave and say "hi, please take a look at me", it then evolved to be used a little more towards look at this new page or "section I made, aren't I great?" The answer was no, you are spamming search engines and crawlers.
Eventually, although the tool was and is still there it's become near worthless, its a nice prod to search engines but pretty useless. Search engines will take into account your asking but it will also use what it normally does, search discovery.
Search Discovery is where a search engine spider / robot will follow a link from a website to a new or existing website - and then index that page. This is how modern search engines work and crawl the internet, spiders crawl across the links of the web to find content - thus making it a "web" of pages.
In addition to Search Discovery, search engine submission has been replaced by sitemaps. One of the first things a search engine will do is check your domain for a sitemap file. Once it's found one it knows where your important pages are, when they were updated and about the architecture of your website. It can then decide which pages to crawl first, and move through your website indexing it over a period of time (relatively proportionate to the size of your website).
So, what's my advice on search engine submission?
<h4>If you are a new website (new domain etc) then do a submission to Google, Bing, Yandex, Baidu and a few directories.</h4> <h4>If your website is not new, don't bother submitting it again.</h4> <h4>Ensure your sitemap is complete and up to date.
Then submit it to Google Webmaster Tools and Bing WT.