Why is Google not indexing my website?

There are four things normally stop Google from indexing a site.

You are telling Google not to index the site – use Google Search Console to inspect some pages to see if they are crawlable and indexable. Usual problem causes would be the robots meta tag or hosting blocking Googlebot.
You have a penalty – Google Search Console should make you aware of this although from experience not always. If you really feel like your site should be indexed maybe reach out to someone via the Google Webmaster Forums.
Google doesn’t know your site exists – here again Google Search Console will help you and you can submit your pages for review. Also, set up and submit an XML sitemap.
If Google Search Console shows your pages are crawled but not indexed then you probably have a value problem and Google simply doesn’t feel your content is worth indexing. One good link from an external site can fix this or you may simply need to bolster your content. My top tip here would be to take a genuine view on whether your site adds anything of value that Google should be interested in. If it doesn’t, find a way to make it so it does.