Links to your site from other sites are extremely important if your site is going to perform well in search engines.
Google actually counts the number of inward links to your site from other sites - and treats each link like a "vote" for how important your site is.
If you consider big important sites like bbc.co.uk or amazon.co.uk, these will have a lot (millions) of incoming links. Even without being able to understand the content on those sites, Google's link-counting systems will identify the sites as extremely important, just based on the number of incoming links.
After a brand new site has been indexed by Google, all that Google knows is that it is a new site with no links in from other sites. Consequently, Google is unlikely to place the site high in its search results pages compared to other well-established sites.
So, we recommend that you take every opportunity to promote your web address and get as many other sites as possible to link back to you. Here are some ideas to get you started:
The only thing to watch out for is that Google does not particularly like paid directory sites and "link farms". The worst examples of these are unlikely to be used by real users and have pages containing lots of completely unrelated links solely for the purpose of tricking Google. If you're unsure whether any specific directory is worth having a link from, ask yourself whether any real human beings would ever find the directory useful - if the answer is no, you're probably safer not to be included in that directory.