The web server can buffer requests and responses, protecting the app server from "slow clients" - HTTP clients that don't send or accept data very quickly. You don't want your app server to do nothing while waiting for the client to send the full request or to receive the full response, because during that time the app server may not be able to do anything else. Apache and Nginx are very good at doing many things at the same time because they're either multithreaded or evented.
Most app servers can serve static files, but are not particularly good at it. Apache and Nginx can do it faster.
People typically set up Apache/Nginx to serve static files directly, but forward requests that don't correspond with static files to the app server, it's good security practice. Apache and Nginx are very mature and can shield the app server from (perhaps maliciously) corrupted requests.
Why can some app servers be directly exposed to the Internet?
Phusion Passenger is a very different beast from all the other app servers. One of its unique features is that it integrates into the web server.
The Rainbows author publicly stated that it's safe to directly expose it to the Internet. The author is fairly sure that there are no vulnerabilities in the HTTP parser (and similar). Still, the author provides no warranty and says that usage is at own risk.
Application servers compared
In this section I'll compare most application servers I've mentioned, but not Phusion Passenger. Phusion Passenger is such a different beast from the rest that I've given it a dedicated section. I've also omitted Trinidad and TorqueBox because I do not know them well enough, but they're only relevant anyway if you use JRuby.
Mongrel was pretty bare bones. As mentioned earlier, Mongrel is purely single-threaded multi-process, so it is only useful in a cluster. There is no process monitoring: if a process in the cluster crashes (e.g. because of a bug in the app) then it needs to be manually restarted. People tend to use external process monitoring tools such as Monit and God.
Unicorn is a fork of Mongrel. It supports limited process monitoring: if a process crashes it is automatically restarted by the master process. It can make all processes listen on a single shared socket, instead of a separate socket for each process. This simplifies reverse proxy configuration. Like Mongrel, it is purely single-threaded multi-process.
Thin uses the evented I/O model by utilizing the EventMachine library. Other than using the Mongrel HTTP parser, it is not based on Mongrel in any way. Its cluster mode has no process monitoring so you need to monitor crashes etc. There is no Unicorn-like shared socket, so each process listens on its own socket. In theory, Thin's I/O model allows high concurrency, but in most practical situations that Thin is used for, one Thin process can only handle 1 concurrent request, so you still need a cluster. More about this peculiar property in section "I/O concurrency models".
Puma was also forked from Mongrel, but unlike Unicorn, Puma is designed to be purely multi-threaded. There is therefore currently no builtin cluster support. You need to take special care to ensure that you can utilize multiple cores (More about this in section "I/O concurrency models").
Rainbows supports multiple concurrency models through the use of different libraries.
Phusion Passenger
Phusion Passenger works very differently from all the other ones. Phusion Passenger integrates directly into Apache or Nginx, and so can be compared to mod_php for Apache. Just like mod_php allows Apache to serve PHP apps, almost magically, Phusion Passenger allows Apache (and also Nginx!) to serve Ruby apps, almost magically. Phusion Passenger's goal is to make everything Just Work(tm) with as little hassle as possible.
Instead of starting a process or cluster for your app, and configuring Apache/Nginx to serve static files and/or reverse proxying requests to the process/cluster with Phusion Passenger you only need to: Rubyonrails服务器英文文献和中文翻译(2):http://www.youerw.com/fanyi/lunwen_77918.html