First things first, there are three main ways to attract traffic to your website. What you're asking about (backlinks resulting in higher rankings is just one of them).
- Search engine optimization
You find keywords, which are relevant, often searched for and face little competition.
You write great content and make your site overall appealing to users.
You build links with keywords (a much broader spectrum that a couple of main ones) in anchors.
You eventually get high ranking. And traffic.
2.Search engine marketing
Your traffic are people clicking pay per click ads.
3.Driving traffic directly
That is so-called referral traffic. People come to your website through a link you (or somebody) else leave elsewhere.
How can you get referral traffic? Here are some options for you:
(a) forum marketing. You help people on forums (relevant to your website thematically) answering their question in detail and providing link to your blog where you give an even more detailed answer to the question. People think: wow, this guy is knowleadeable and helpful, I'll read his blog regularly
(b) guest blogging. You write an article on somebody else's blog (relevant to your website thematically), leaving a link in your bio section. People think: wow, this guy is an expert and a great writer, I should bookmark his website.
(c) social media. You work at social media engagement on twitter, fb, g+ and such. People come through links you share.