First of all, lets identify how Alexa get their rank. Alexa has a large traffic data panel consisting of millions of people all over the world. Based on the data from this sample, Alexa estimates the number of visitors to all sites on the Internet.
Alexa rank is important in the sense that it provides you high-level data with how traffic and engagement fare on the Internet. While there is no exact range for what defines a good Alexa rank, generally, the lower the number, the better. If your business is seasonal, the peak times of the year might also show a better Alexa Rank than others.
Having the mindset of wanting to improve your Alexa rank is great, but also consider that Alexa rank is dynamic because it has a more narrow focus on looking at traffic and engagement. At one point, the score might be in your favor. A few days later, it may have changed. It would help if you instead looked at your site from a holistic point of view and then drill down to the areas that need the most attention.
Compared to Google's sophisticated algorithms, the ranking system used by Alexa is still in a relatively primitive state. Their system is comparatively easy to manipulate and a single user can affect their Alexa rank in a way that just isn't possible with Google.
Alexa Rank can act as one tool for identifying the popularity of your site, especially in comparison to competitors, yet most digital marketing professionals would agree that Alexa Rank is not something valuable in reference to overall SEO optimisation and performance.
From an SEO standpoint, knowing where your traffic and engagement stand is important. From that point, you can make a plan to optimise your site which, in turn, will ultimately increase your Alexa Rank too.