Relevance
Relevance is how well a business matches what somebody typed. If the search names a job and a town, the business with a page about that job in that town is a closer match than one with a home page mentioning nine services.
This is the one you have the most control over. It comes from what your site says and what your Google listing says, and it's the reason a smaller company with better pages can sit above a bigger one with a thin site.
Distance
Distance is how far your business sits from where the search happened, or from the town named in it. You can't move your shop, and you shouldn't try to fake an address somewhere else. Google's rules don't allow a location you don't staff, and a listing taken down is worse than a listing sitting fourth.
What you can do is stop letting distance be the only thing Google knows about you. A real page about the work you do in that town gives it a relevance reason to show you there, which is the lever distance leaves you.
Prominence
Prominence is how well known a business is, on and off the web. Reviews feed it, so do mentions of your business around the internet, and so does how well your site does in ordinary search results.
It's the slowest of the three to move and the one people waste the most money on. Buying links or reviews is named in Google's spam policies, and a business that gets caught doing it has a bigger problem than the one it started with.
The honest version is steady: reviews from finished jobs, a site that's genuinely useful, and your name in the ordinary places a local business turns up.
What the order doesn't tell you
Google shows a different list to somebody standing in a different town, and it changes what it shows over time. The order you see on your own phone, in your own driveway, isn't the order a customer twenty minutes away sees.
Nobody can promise you a position, and any company that does is selling something Google says in writing cannot be bought. The work is to be a better match in more towns, and to let the order follow from that.