There are entire courses taught on this subject, but I'll try to be brief.
Appearance: the look of a website has a huge impact on its success. It's the first thing people see. And the theme must be appropriate — a group of men in business suits would be great for an employment agency, but terrible for a site pushing outdoor adventure.
Usability: it goes without saying that a site must be user-friendly and intuitive. If visitors don't know how to find what they're looking for, they'll bug out. The temptation to hit the back button is every site's worst enemy.
Fast loading time: the site has to load fast. If you've ever clicked on a link, and the site locks up your computer while it loads every api and pugin that it needs, that site isn't going to last long. Same thing with tons of images. A good site is optimized to only load what it needs to function. 6 to 10 second load times are usually the kiss of death.
SEO: Search Engine Optimization is creating content that answers questions that people are typing into Google. It focuses on keywords that match what people are looking for. A good website will know its audience, and hit the top search results using those keywords in the text part of the page. Search engines see those keywords again and again, and rank the site among the most relevant results.
Killer content: SEO is nothing without good content, so successful sites hire the hottest writers to provide that content. They use SEO to hit the top search results, and provide valuable info for people looking for it. And the most successful sites change their content to stay relevant and keep their users satisfied. If you keep visitors happy, they'll keep coming back. Good content builds trust.
A memorable URL: People have to know where to find you, and that's where effective domain name choice is key. So, .com is by far the most common, and what many think of when trying to remember a web address. .net is popular as well, .org less so. The name must also be simple, so no hyphens, weird characters, or capital letters. Also most sites are no more than 15 characters.
Obvious contact info: it might go without saying, but visitors need to know how to find you. Make a phone number, email, address and a contact form easy to locate.
An effective opt-in strategy: A fancy name for getting people to sign up for an email list. Typically the best sites offer something of value for your email address, like a free e-book, or the results of a quiz you took. Once they have your email, they can send you a newsletter, maybe with helpful tips, or links to interesting content.
Now, I could go on for ages about image hierarchy, optimized layouts, and microcopy, but that's way too much detail. There's a lot to a site's success, but these are the main drivers. Hope this helps.