There are several tactics that will help improve your Alexa Rank:
Produce engaging, original content, updated frequently that provides real value to your audience. Content that strays from this motivation fails to build loyal audiences. When readers find resources valuable and informative, they engage with future content and share among their networks (link building), introducing new visitors that potentially turn into customers.
Get more related sites to link to your website. Otherwise known as inbound links, this tactic helps search engines clearly define your niche and also increases the trust and quality of your site.
Internal links, on the other hand, are links that lead from one page or post on your site to another. These are beneficial because they guide visitors through your website (i.e. website navigation), keeping them engaged with relevant and related content.
In all, both inbound and internal links help search engines understand the content of your site(s) and determine how valuable it is to visitors.
Find keywords that are driving traffic to your competitors and optimize your site for them, or buy PPC campaigns for those keywords. By doing a little keyword research you can understand what your audiences are searching for and how.