A landing page is simply the page which someone arrives at after clicking on a link. It can be your website's home page or any other page. In the affiliate and online marketing world, a landing page is typically sales driven so that when you send traffic towards that landing page it works to convert on whatever goal that you have for it whether that's to sell a product, get someone to sign up for your mailing list, etc.
A lot of work can go into getting a landing page just right in terms of design and copy and seasoned marketers will oftentimes tweak and split test their landing pages over and over in order to better convert on their goals. This is especially true if you're using paid advertising, because the page which you are sending someone to when they click on your ad is referred to as the landing page, so getting your landing page just right is essential not just for converting on your goal with that visitor but for pleasing the advertising system, as well; thereby typically lowering your cost per click.
The concept of landing pages are better understood when identifying the different styles of pages, so let's go over the most common and best landing page examples.
Sales Letter Page - Sales letter pages are what product publishers use most often. This type of page is used with the express purpose of selling to the visitor while on the same page. You've probably seen one of these pages before; a very long vertical sales letter page on which you can use lots of testimonials, detailed information on that product, videos/photos, and other kinds of multimedia to better sell to your visitor and convince them of their need for your product.
Review Page/Click Through Page - Unlike with the sales letter page, on a review page you're "pre-selling" because you're going to link to the product's official sales page from your review page and that's where the heavy selling is done by the owner of that product. A lot of marketers use review pages because generally it's the best landing page for pre-selling, and oftentimes potential customers need this preliminary soft sell before they're ready to purchase. This puts them in the purchasing mindset when you finally send them over to the official sales page and the "one two punch" effect which this creates is very effective.
When it comes to plain and simple selling, I believe that review pages make for the best landing pages as nothing beats that combination of effective review page plus effective sales page.
Squeeze Page - A squeeze page is a static page meant primarily for capturing leads which means getting your visitor to submit any kind of information which you want whether that's their email address or even just their zip code.
Squeeze pages don't have much to them, just usually the content itself (oftentimes in the form of a video) and the form field where the visitor puts in their required information. The page is typically otherwise barren so that the emphasis is on the sign up box without giving the visitor any other options or places to click. Marketers usually offer their visitors some kind of free incentive to motivate the visitor to share their information.
Launch Page - A launch page is something you use typically before a product is launched. It's used to give a teaser about that product and build excitement and this page can be combined with a sign up form similar to the squeeze page so that you can get your visitor's information so you can keep in touch with them and give them updates as the product comes closer to launching. By correctly building the anticipation with the launch page, once that product launches you will get a lot of sales right out of the gate because of your efforts on the launch page.
Viral Landing Page - A viral landing page is a page on which you have content which is worthy of going viral (duh). If you come up with a really fun game or useful app, really any kind of fun/interesting content which is easy to spread (hence viral), you can generate tons and tons of viral traffic to that page. This is a great way to promote brand recognition and awareness, assuming of course you make it apparent what your company/website is and does on that page.