To expand on what Maneesh said, Eclipse itself doesn't know anything at all about
J2EE or Tomcat. However, one of the standard Eclipse downloads does come with J2EE development support plug-ins pre-installed. One of those plug-ins is the WTP plugin and it can run Tomcat, although it does a horrible job of it. Which is why Maneesh and myself prefer to install the sysdeo Tomcat plug-in and ignore WTP server/webapp management altogether.
There are, I think, other Tomcat interface plug-ins out there as well, but I don't have firsthand knowledge of any of them.
The secret of how to be miserable is to constantly expect things are going to happen the way that they are "supposed" to happen.
You can have faith, which carries the understanding that you may be disappointed. Then there's being a willfully-blind idiot, which virtually guarantees it.