Services provided by SEO companies appear to vary a great deal. In essence, any self respecting SEO practitioner should provide you with a detailed plan of what needs to be done. This should comprise of an initial phase during which on-page issues are addressed, ensuring there are no errors, that the images are the best formats and properly optimised, making sure that there are detailed 'rich snippets' present and that the site or page is well designed and caters for mobile devices.
Next, all the anciliery connections to the website need to be created or reviewed. This includes setting up business 'places' on Google and Bing, search consoles on Google and Bing, Google Analytics, social media accounts etc. etc.
Next, there should be a plan to implement a set of quality backlinks and citations and initiate a marketing campaign through one or more mechanisms. There should also be a monitoring element included by which you can measure the relative success of your campaign.
Many SEO companies do not provide all of these elements. It is quite common for SEO plans to only contain backlink building. This is because the task can easily be offloaded to cheap labour in Asia at a fraction of the cost. Easy profits, and no accoutability. Always insist on a detailed plan when engaging with an SEO provider, you must have some means of measurement to know where your money is being spent, otherwise you will have no recourse when things don't work out.