Apache was designed in an era where the webserver did everything, and most of what it was doing was serving static content. And the fundamental design of apache as well as the design of its configuration system is optimized for that. And though it's been modified extensively to do everything a modern web server needs to do in many ways it's still held back by that heritage. Also, apache is fairly monolithic. The way to add functionality to apache is generally with modules, for example, and generally a random apache installation is going to have vastly more features active than you may actually need, or want. All of which affects performance.

Nginx was written from the ground up in the modern web era, when we had already learned about the common ways that real websites worked (dynamic, high throughput, tied into other technology like php or rails, possibly living on multiple servers, etc.) Nginx is designed for efficiency and low overhead. It's also designed to live within an ecosystem rather than live as the container of an ecosystem, at its heart it's not a web-server it's a proxy. And all of this makes nginx easier to set up, easier to configure, and generally more efficient with superior performance compared to apache.

Here's an example. I have a server set up with a couple different sites, some of them are fronted by varnish (for caching), several run on php, and another runs on rails. With nginx this is all fairly easy to do. Instead of installing modules as you would tend to do with apache you set up php and rails as standalone socket-based servers (e.g. php-fpm and unicorn) and then in your nginx configuration you simply tell the web server where those are and how to use them.

Nginx also funnels you into a pattern which makes it easier to scale. Because nginx is just part of an ecosystem and not the container of an ecosystem you can easily migrate components to other servers as necessary. In my example I could push varnish off to another server, push each php app off onto its own server, push rails off onto separate servers, etc. The configuration changes would be fairly minimal and it would all still just work.

It's simpler, easier to configure, has event-driven "magic" :). But seriously, you can google this and it doesn't make sense to sell HTTP servers like toothpaste anyway.

Just be absolutely sure that you never need the additional features that Apache Httpd provides, and Nginx will probably be a good choice.

Read http://stackoverflow.com/a/3635081/309483 There is also a linked 100+ vote question, but I think it has too much noise.

I'm an Apache guy too. If you know how to configure it, there's not much reason to switch from Apache.

You probably don't need to. Apache is good enough and if you have to sell your boss on using Nginx then you probably don't have enough need to switch. It should sell itself or you are probably just wasting your time.

I use Nginx because I find it easier to configure and more lightweight out of the box.

It's not so much switching to something qualitatively better than to something with a somewhat different style.

For example, Apache is chock full of modules with a certain richness to them, they do everything and everything you could possibly think of, with a verbose configuration that usually comes filled with "defaults" by the maintainer, and plenty of options to choose between processes and threads; Nginx is "lean and mean", strictly event-based and minimalistic in almost every way, is usually compiled to include just what you need (and still feels un-monolithic despite modules being statically compiled), comes with sensible defaults and is usually bundled with almost no config.

Some rough analogues: Nginx is to Apache what (Varnish, Postfix, Go, Git) is to (Squid, Exim, C++, Subversion).

Its more efficient. It uses far less RAM when handling a lot of concurrent connections.

If your using it already, why do you need to sell it?