Off-page SEO builds a website’s reputation and authority by connecting it to other high-quality websites. Off-page SEO techniques include: link building (acquiring high-quality backlinks) from other websites and managing local listings and directory profiles. When many websites link to a brand’s website, it shows search engines that the brand’s website is trustworthy, reliable, and reputable, which increases its search rankings.
While most of the links to your site will be added gradually, as people discover your content through search or other ways and link to it, Google understands that you'd like to let others know about the hard work you've put into your content. Effectively promoting your new content will lead to faster discovery by those who are interested in the same subject. As with most points covered in this document, taking these recommendations to an extreme could actually harm the reputation of your site.
QUOTE: “Starting April 21 (2015), we will be expanding our use of mobile-friendliness as a ranking signal. This change will affect mobile searches in all languages worldwide and will have a significant impact in our search results. Consequently, users will find it easier to get relevant, high-quality search results that are optimized for their devices”. GOOGLE
Ask for a technical and search audit for your site to learn what they think needs to be done, why, and what the expected outcome should be. You'll probably have to pay for this. You will probably have to give them read-only access to your site on Search Console. (At this stage, don't grant them write access.) Your prospective SEO should be able to give you realistic estimates of improvement, and an estimate of the work involved. If they guarantee you that their changes will give you first place in search results, find someone else.