SERP(Search Engine results Page)- search engines cache SERPs for frequent searches and display the cached SERP instead of a live SERP to increase the performance of the search engine. The search engine updates the SERPs periodically for new pages, and possibly to modify the rankings of pages in the SERP. SERP refreshing can take more or less time to update.
SERP, short for "Search Engine Results Page", is the listing of results on search engines in relation to a query using one or more keywords that a user has entered. The pages of results that you will see are the SERPs. Whether or not you think that SERPs are important is up to you. If you have a website however, and would like it do well, it is the positioning of your website in the SERPs that should be of prime concern to you. Simply put - if a user can't find your site, how will they ever visit your site ?
I am confused in this question. I not know that what is your question actually. SERP is search engine result page only. It is only a page.
To gain SERP you need to do lot of backlink building by doing article submission and forum and blog commenting.
SERP is ranking measurement in search results. For example, if I search "cat food" in Google.com, I will be shown 10 results. Let's take "Whiskas" is your site, then your current SERP ranking is #6. Usually, SEO job is to increase SERP ranking from current ranking to higher spots (in this case top 5). You need to implement SEO strategies (there are over 200 factors involved in measuring SERP ranking for Google algorithm) to increase current ranking. This is connection between SEO and SERP. Hope this explains your doubts.