External SEO is concerned primarily with how your website is being linked or referred to.
Your backlink profile plays a huge role in helping the search engine to understand the quality and trustworthiness of your site.
If a link is from a high quality website, it's likely to be seen as a vote of trust, likewise if the link or the linking website is of a low quality it can have a negative effect. So, with that in mind it's important to make sure where possible that your links are of as high quality as possible.
Links from external websites always play an important role in determining how valuable one website is in comparison to another. Where possible, it's recommended that any external links are altered to reference the new destination URLs. This will save a search engine having to go through a redirect before reaching their final destination, and can therefore mitigate negative effects of additional load speed, algorithmic damping, etc.